Should I quit trying to get my 89-year-old mom to do more activities, although she has lost executive functions?

Boy if any two people were candidates for asst. living I don't know who that would be. Your dad needs 24/7 help and support, and your mom could use some outside stimulation as well. I don't know why folks think that asst. living is such a slap in the face and makes them feel like they're being put 'in a home'. It would be so much less stressful for both your parents under these circumstances to let other people take care of them for a change. Other than that, I'd say your mom's brain has been damaged and she is no longer capable/willing to do what she once did. For their age, I think they're doing dang good if you ask me.

You are at the point where I was before I made the decision to transition Mom to ALF care. She does not have cognitive issues but has lost a lot of her mobility and desire to do things. I found that I could not make her do things that she did not want or could not do. I just tried to surround her with hobbies, music, etc. that she could still manage and do on her own time. If your Mom is content to sit, let her do it. But, it is important that she continue with her exercise.
Your Dad needs 24/7 support now, that is why naheaton suggested assisted living. It is getting to hard for him to handle both the stress of Mom's issues plus the activities of daily living. Also, most ALFs have lots of activities and social interaction that would be great for both your Mom and Dad.
You could try more in-home care - tried that myself but ran into the same issues as you. Some were unreliable, there were scheduling issues, and times they could not show up. You can use an agency, but that gets expensive too.
If you are committed to "aging in place" for your parents, you may want to contact your local ALFs and speak to the director and ask about aides who can also help patients with cognitive issues. Also, your doctor can write a prescription for physical therapy for your Mom. She would have to go to their facility unless she has had an injury or hospital stay recently. Is she able to get out?
In the last year I have seen more decline in my Mom. She cannot handle overstimulation and becomes frantic when someone tries to get her to do something - even when it is for her own good. So I understand what you are going through.

Appreciate the comments so far. We have not ruled out ALFs completely, but my parents live on the farm they still own and manage. Someone does the farming for them, but my dad especially enjoys keeping an eye on things, going out to the field to check the crop, etc. He would not be happy away from home, and don't think Mom would be, either--unless she declined quite a bit, he wouldn't want them to be separated (we took him to see her everyday during her hospital and rehab stays after CA was diagnosed). Although she has changed somewhat, they still are most happy being in home with each other. They also love seeing their grandkids and daughters multiple times daily, as we are right next door.
My husband and I sold our home and moved down here specifically to help; I am not working, and only in the last couple of years have had to step in as we thought I would. My sister and I have a pretty good division of labor (finances, cooking, transportation, meds, etc.), which is a blessing. Our understanding is that my dh and I will move into Mom and Dad's home when needed, which hasn't been yet but may be soon. Mom and Dad do lament the loss of their independence in things and keep telling us they don't want to be burdens on us, which is also why we haven't insisted on taking over things until we see they are needed.
When I say they are doing well for their age, (particularly my dad), it is an understatement. His grandma lived a very active, mentally sharp life until she died at 103, and he may be on the same track, unless his diabetes worsens, which is our main concern. Mom uses a wheeled walker for balance and has gone to PT for balance and strength, recently to work on her dominant hand, which was either affected by stroke or tumor and does not fully work. These are discouraging to her, I know. I would just like to encourage her to try to find a sense of worth and capability in doing some tasks and/ or hobbies, even though they aren't the way she used to be able to do things. If this is to happen, it probably means me making the commitment to spend more time trying to motivate her or get her into a routine where she is reminded to help Dad more. She is not that antagonistic, but the "slavedriver" term will come up, and I need to have a good sense of humor and a bit of a thick skin going into this, I know.

Kathmom, you seem to have exceptionally good insight into the situation. Your basic question -- how much to encourage Mom to be active and how much to allow her to just rest -- is one a lot of us face. In early stages of at least some types of dementia, stimulation is positive and helps promote well-being. As the disease progresses oversimulation is more apt to be a problem. Discuss this issue with the doctor who is treating your mother's dementia. What is realistic to expect in this kind of dementia? Will repetition create habits, or is it likely she will always need cues about what to do next? The more you know about her particular kind of dementia, the better armed you will be to make decisions you'll be happy with.

I think that you have hit the nail on the head when you say, " If this is to happen, it probably means me making the commitment to spend more time trying to motivate her or get her into a routine where she is reminded to help Dad more."

You moved close so you could provide more help. Fortunately it wasn't needed as much as you expected at first. It sounds like the time has come. Perhaps it isn't necessary to move into their house yet, but more active participation may be needed.

It may also help to shift expectations a bit. Maybe the dinner dishes can sit until the the daytime aide comes in. Maybe the grandkids can take turns helping Gramma do them each evening, and then play a game of checkers with Grampa. Maybe you don't live with them, but you do eat the evening meal with them, as a family, once or twice a week, so you know it is on time and appropriate for their needs, and you and Mom cleanup together afterwards, or she keeps you company while you do most of it.

They need assisted living. It sounds like you are positioned to provide that in their own home, if you are willing to take on that role. Hire more helpers -- AL facilities have a staff, not a single person, to provide assistance.

It sounds like you will make a conscious decision about how to proceed, and not just follow the path of least resistance or wait for a crisis. You are going a great job in the caregiver role. Keep it up!

You might want to look at 24/7 live-in type care from a senior home care company. That does not mean that someone would actually Move IN with your parents, but that the caregivers would be assigned in 24 hr shifts, to sleep when your parents sleep, with the use of a baby monitor or motion detector alarm, so the caregiver can be alerted when a parent gets up. The advantage of that type of agency provided care is that is it MUCH less expensive than hourly around the clock care, provides full coverage for their safety, and provides continuity of care with only two or three caregivers per week.