Is this fair for me to drag my kids to the emergency and urgent care?

It's depressing you too. Next time you call 911 and have them pick up Dad. Your sister is the center of her own universe, so ignore her complaints. Dad sounds like he would do better in Assisted Living than being alone. Once he moves there he will have a lot of fun with peers and good food.

Do not take your kids to Dad's appointments.

He is able to care for himself, but he suppose to limit his salt intake and make healthy eating choices, but he doesn't! So when I have him at my house I cook healthy meals, that means breakfast, lunch, dinner, and snacks! If I don't bring him over to my house my sister will complain that I need to come over to his house and cook for him! I can't win, it makes more sense to bring him and watch everyone at the same time versus bringing all the kids to his house. Seriously, my sister doesn't work or have kids and she makes excuses like " your a better cook then me"! I need a break or I'll be the next one in the hospital sick. My sister also says that her therapist said she shouldn't spend too much time with dad because it's depressing her.

FF, the OP posted another longer post on the same issue:

https://www.agingcare.com/questions/Should-I-be-taking-my-kids-to-my-sick-dads-DR-appointments-185660.htm

Can we have more information about your Dad, is he able to take of himself on the other 3 days when he isn't at your home? If yes, maybe you could cut back on the number of days he is with you.

As for you having to bring all the kids with you for your Dad's doctor appointments, see if your sister could babysit since he is tired of going to his appointments [many of us can understand that, like if we see one more waiting room we will scream].

Just because your sister has no children [which was her choice] it doesn't mean she doesn't have a house to clean or groceries to buy. Yes, you have more cleaning and more groceries, but that was your choice.

See if you and your sister can work as a team, to help each other out more with your Dad's care. If it becomes too much, maybe it is time to get Dad another level of care, like a paid caregiver to come to his house.