Can power of attorney be changed if the parent and the legal guardian do not get along anymore because of the sickness?

Are you afraid that your mother will withdraw the POA she has granted you and put it in the hands of a less suitable person? I suppose that if she is "in her right mind" she has the legal right to do that. Or are you wishing to hand it off? As Lilli says, it does not obligate you to any particular course of action, just to make decisions on her behalf (or hopefully to carry out decisions she has made ahead of time) in the event she cannot make the decisions herself.

Which brings up the question of her mental state. Does she have cognitive impairment? Dementia? Do you think she is still capable of making decisions?

Who would she have for POA if she revokes it from you?

Power of attorney just gives the "agent" the ability to act on behalf of the parent in case of incapacitation. In other words, you are acting on the decisions that your Mom already made. It does not direct your care of her.
You could keep the POA to help out with financial and extreme medical decsions. However, your Mom needs another placement and you need your sanity back. Caring for your parent does not mean that it has to be in such close proximity. On your own, start collecting information about ALFs and NHs and visit them. Get recommendations from doctors, friends, and others who have parents in these facilities. Then you are armed with some concrete ideas and plans.
Everyone wants to stay in their home until the end...not a realistic result for most people. Once you find a good fit for her, start the ball rolling, make a timeline, and keep reinforcing to your Mom what a good idea it is. Once she sees that you are not backing down, hopefully she will focus on her new life. And you can go back to being the caring daughter.
Even in the best circumstances, I think that it is very hard to combine two households; whether that be having a parent or adult children (and their children) move into your home.
I don't think you are trying to escape the requirements of having the POA, but the day-to-day care of a seriously ill parent who needs more medical and physical care than you can provide.
Good luck...let us know that you made one small change toward your goals.