What happens in the process of calling a local AOA?

Maybe you've seen me more active as of late. I made a promise to myself last year I was going to find a way out of here, out of this role, and out of this house. It's been too long, too much F.O.G., and tired of the feeling of constant desperation and constantly doubting my sanity, my need for freedom and what happens if i leave. I could stay, but I really don't want to. I'm being weaker in certain ways trying to be assertive and end up being aggressive and the only one hurt.

I've already got deep plans about where to go, When, is hesitant for multiple unpractical and practical reasons, but it will be a hard no longer than May. Also I know I will definitely need therapy once I leave here. I'm looking into that also with the area to live. I honestly don't think I would be safe with myself if I leave without a support to work with. So therapy will be that.

The biting issue that has me feeling absolutely torn is, what to do about my parents... My dad is 68 i believe (i don't keep close track of ages as much), he has mobility issues (no feeling in the feet and weak legs, which has him bed and wheelchair bound when going to appointments), I suspect dementia on top of his naturally demanding and shifting personality (he's always been that way, but the stroke he had years ago and this possibility make it magnified and predictable, but not easy to deal with). He needs a lot of physical care, but refuses to do some things for himself unless i aggressively refuse (which is psychologically harming me and not him). Also I'm not as strong physically (even with exercise) as I was in high school. It's hard to shift his weight in a sling these days and I no longer what to do that much longer for both of our sake. Mom is 70 something, has arthritis in the hands, has to use a cane intermittently for knee troubles, and possibly dementia or something slowly creeping up on top of her natural personality similar to dad's but not as frequent (she's a little easier to deal with these days). She has limited hand strength, but is able to cook, do a little dish washing, and sweeping. Her mind is ok enough to do dad's medicine, take care of bills and she's able to get around more with my assistance to drive her to appointments, errands, etc.

Knowing this, exactly what is the experience you may have had with calling an AOA (Area on Aging). What happens? How much of my or possibly my brother's involvement is necessary? And if say they need to place my parents, could they place them in the same facility or is it a chance they'd be separated?

Any answer can be helpful. I'm really trying to get a good idea of what may happen. I may not like, or even stand them at times, but I am not the type of person to be a "butt" and abandon them. No matter how much I feel that, I cannot bring myself to do such a thing. It's the decent thing I can do for them as human beings.

One last thing, if there are other agency I should investigate that you may know of, I'm interesting in hearing it. I have to balance this fear with some rationality. Thank you all.