How do you handle when the suggestion is always that you, the caregiver, need to do more!?

He is living in an AL community.
Check their "social calendar" and see what activities he might enjoy and encourage him to follow through. Contact the Activities Director and tell them that "dad", Mr. DoingMyBest73 would like to : Go to lunch with the Group on Tuesday, Go Bowling on Wednesday morning and go on the Outing scheduled for Friday afternoon.
I am sure that if he does half the things that he finds interesting that by the weekend he will be exhausted.
Tell Sis that she can also access the Activity Calendar and suggest things for him to do TO him.
If he chooses to follow through great, if not and when they come to get him for the activity he declines that is on him.

One option might be to ask sister to research options for a carer to take him out for these weekly excursions, either at his expense or hers. She organises it by phone, including payment and transport options. When she’s found something appropriate, perhaps you offer to meet the caregiver yourself, just to check them in person. But it’s her idea, and she carries it through.

It would be interesting to see if she does! Telling you what to do is very different from her managing it herself, as you both may discover.

Just say no. He cannot make those type of demand. If he's bored so be it or let your sister come to visit or send him to her house. One adult child with a family can't do it all.

Beatty here always says that there will be no solutions as long as YOU are all the solutions.
Is your father capable of understanding when you speak with him? If he is, simply do so.
If you need some help with the POA, do seek it; your Dad's funds pay for this; you could hire a Fiduciary to do, say, all the bills payment and record keeping for taxes and etc.
You need to set your own limits with your Dad. There is simply no one else to do that for you. Tell him that you cannot take him to the Museum, and that you are sorry, but your own family has needs you need to fulfill, and you need some down time of your own.
I was POA and Trustee of Trust for a wonderful man, my brother. My brother had a diagnosis of probable early Lewy's and he hated it, but he had to ask me to take over finances for him, bill paying, and etc. It was a JOB and that in a simple estate with a very well organized man. He was in Assisted Living at the other end of the State. I would have loved to be in a position where I could go to a weekly or semi weekly dinner with him, but that wasn't possible. And I would NEVER have left a relationship I treasured to descend into obligation.
I would speak with family first about all you are doing, and about the pressure you are feeling. Start with Dad and see how that goes. Might he have a bad reaction? Sure. But that's life. We cannot live our lives to make others happy at the expense of ourselves and our own nuclear family.
If speaking with Dad, with Sister and Dad if necessary, doesn't work for you, or if Dad is incapable of computing the realities, you may need a few counseling session to get clear in your mind that your own human limitations is nothing to feel guilty about. You may feel grief that you aren't the good fairie complete to the magic wand, but you aren't.
Embrace your limitations. Hold them dear. When you have done that, share them with the family. And stick to your guns. Wishing you the very best.

Take a page from my husband, who nods and smiles thoughtfully at my many excellent suggestions . . . and then he goes and does whatever he wants. ;)

But if you want to engage:

Years ago, I led a controversial cause, and hostile media training taught me how to cope with reporters’ questions I didn’t want. You have to answer their question briefly, and then bring your answer around to what YOU want to talk about: “Yes, that’s true and we’re addressing that, but the important thing to remember is . . . “ whatever I wanted to get out there.

Acknowledge your dad’s concern, valid or not, then make it about you. “Gosh Dad, I’m sorry you’re bored. We always enjoy seeing you on Wednesdays. When we have dinner this week, we can tell you all about how Little Sally got the lead in the school play, and she’s only a junior!”

Repeat after me: not my circus, not my monkeys. Keep the conversation about your circus.

Good luck!

No, you do not have to arrange your father's weekend entertainment.
Your sibling is the one who shot her mouth off and put the idea in his head about getting out more because it's spring.
This sibling can arrange and pay for a companion to take your father to the local museums and attractions on the weekends.
Posts like yours really get my anger up because there are few things in this life that I hate more than being volunteered for something because it's convenient for everyone else. Of course, I haven't been volunteered by anyone in a long time. My response when I see it approaching is two simple words. Just seven letters combined. The first starts with an 'F' and the second starts with a 'Y'. I would strongly encourage you to learn these two words and not to be shy in using them when the conversation starts leading towards you being volunteered.
As for your father, tell him plainly that you will be entertaining him on weekends. No explanation is necessary. Offer to sign him up with your town's senior center. They usually send transportation. Or you'd be more than happy to hire a weekend companion that your sibling will pay for to take him to the local attractions and museums on weekends. Then give him a phone and have him call that sibling who ran her mouth and work out the details.
Stop letting your family walk all over you. You do enough for your father and enough IS enough.

You need to let your sister know that you can't do this. My sibling is in another state and expects me to visit regularly. Like you, I have a full-time job, have two teenage kids, etc. My sibling always asks for me to visit my mother more, but I would have to give up more weekend time, which is the only free time I have. He only comes out once a year, so I feel has no say in what I do.

I would be very clear with your sister and just say NO. My mother has needed care for a decade and if I had spent as much time with her as my brother expects, I would have not been able to raise my own kids and work to secure my own financial future. Not to mention I would be a miserable person.

If your father is bored, ask your sister to come out more regularly. She could come out and take weekend responsibility.

I don't know if your sister said what she said just as a way of conversation prompted by your father (he said he was bored and she just started spit-balling) or if she offered it up as a serious consideration, clueless how involved you are and how much time and energy it takes. Either way, he took it seriously, and now it's in your lap.

You do enough. More than enough. It drives me crazy when people who need help just keep dumping on those caring for them without a thought of how it impacts EVERYTHING. Let's not make anything easier for the caregivers....

If your sister or someone else offers more suggestions how you might help your father, maybe you can turn that around: "I help Dad a lot, more than you probably realize. With only so many hours in a day, it would helpful if you took the time, like I do, to do what you're suggesting. Dad would absolutely love time with you."

Hey, maybe she can plan her vacation to visit him, take him to a couple doctor appts, some museums, shopping....Maybe you can make that a suggestion to her (if she seriously believes you have the time to do the things she said).

Hugs.

Your Dad is in an AL. They have activities and outings. Moms had entertainment too. He is there because you cannot provide him with these things. I think the elderly (no Dementia) forget was involved with raising a family and working f/t. Working is not just 8 hrs a day, its at least 10. The hour before to get up and ready and driving time, the hour after to get home, lets say. So your up at 6 and home by six, lets say. Gives u 5 hrs to cook a meal, take kids to where ever they need to go or picked up from. 11pm u go to bed and start all over again. Weekends are to do things u don't get done during the week and maybe....some time to yourself.

I would not say anything to sister unless she says something to you. If she does, send her a copy of your schedule. Your Dad, he needs to be reminded that you are not his entertainment. Your family and job have priority. The AL has activities available, if he is bored he needs to take advantage of that. If Sister wants to visit and take him somewhere, she can do it. He cannot depend on you. Thats just how it is.

This topic is so annoying! Yes, people are always suggesting things WE could do to make things better or easier for my mom. SERIOUSLY??? Please give me a freakin' break. My uncle suggests she go to the casino 3 hours from here. Really? She can't drive herself there, we are busy and could care less about going, so......Please just butt out! They just talk on the phone so I know he doesn't really understand the extent of her issues with early dementia.

If your dad lives in assisted living, there is absolutely NO reason that you should need to take him anywhere! If he's bored, it's his own fault. He could be saying no to all kinds of things and then, yup, you'll be bored. If he has cognitive issues, that could keep him from fully participating. You could ask the staff if they can try to get him to do more things. He. can refuse but they often try to rally people to come on down to the activities.

Good luck.