How can I make the transition process easier on my family?

Chloe
How are you “ starting the process”?
From earlier posts I thought I remembered that you were living in GD home? You were primary caretaker as you worked nearby. Your SO was working a distance away.

I think the idea of the letter is a good one if a doctor will write it. It would support your opinions of GDs health. Notice to the POA that you are moving should probably also be in writing. Have you contacted Area Agency on Aging or Adult Protective Services? That might be a proactive measure, letting them know you have a vulnerable elder at his address and you are unsure of his care going forward.
Did you sign a contract with the POA? Are you giving adequate notice?
Make sure he’s safe. Make sure you aren’t breaking any laws and have clearly communicated your intentions. Probably should have a signed proof of delivery of notifications from POA.
And yes, An attorney advising you or even writing the letter for you would be effective if all else fails.
The POA probably doesn’t know what to do herself. Just because someone accepts the responsibility doesn’t mean they have all the answers. But she does have the power to make decisions and you are pretty much making the only one you can make.
About her hating you. That sounds inconsequental in comparison to GDs care. Stay focused on that.
I think you are making good decisions to do what you can to get the POA to take action. GDs Health conditions may not be dire but they are beyond your capability to continue as his caretakers. You get to make that decision, not POA.

I would have his doctor write a letter on the letterhead of their practice stating exactly what is physically wrong with your FIL. Send it registered mail to the POA. Is he alone all day while you work? Tell the POA he needs supervision while you’re gone and you will be hiring a caregiver, billed to her as POA to be paid for out of Dad’s funds. If she denies this, she is denying him safe care and could have her POA revoked. If the money isn’t there, she will need to file for Medicaid for him. Saving money for inheritance might be her basis for not wanting him put in a facility. You can also contact an attorney who may be able to help.

I think that it would be a good idea first to give your aunt a better idea of what you are doing. Perhaps you could invite her to stay for a weekend, and be present during all the tasks you do - even do some of them herself. If you don't have a suitable spare room, you and your SO can to a motel for the night, or stay at your aunt's house. To be honest, it would be worth it to spend the night on the floor. At present your LO is not telling her the truth about his needs, and his doctor doesn't know either. No wonder she thinks you are exaggerating.

Put your invitation, with the explanation, into a snail mail letter and KEEP A COPY. You have already written a letter to her, so this might come as a constructive response if she reacts badly to it.

With luck, your aunt will either think you are right, or will come up with a brilliant new plan. If she won't come and you have to leave, go ahead with complaints or take legal action, the copy letter and her refusal to see for herself will be very important to put your case.

I don't quite understand 'she is angry that we are trying to leave'. If you intend to leave the house, she surely has no way to stop you. So long as you give her reasonable notice of when you are going, it then becomes her problem. However as you want to keep relationships reasonable, you need to bend over backwards to help her to see just how difficult things have become for you.

My SO and I are tired. Our POA has a family of her own and does not have time to take care of him or barely even visit him. If we move he has no choice but to go into assisted living and his family(who aren't here helping) want to keep us there so he can stay at homeMy SO was worried that his family would be disappointed in him for not being able to handle it any more but he and I are so exhausted and burnt out that we're not helping our LO anymore. We don't have the time or energy that he needs and craves.
There's no need for law to get involved in any way I just want a clear written letter that will help her understand what we're going through. We want this to be as smooth, painless, and drama free as possible.