How does someone get declared incompetent?

I'm new to the site, have been taking care of both parents in their home for two years...lots of time but no real medical care. I manage their meds, feed them, shop, do laundry etc but they are very grateful and not difficult. Considering that my mom thought I was an ungrateful idiot most of my life (totally not true and never my dad's opinion) I am so lucky she's changed her tune...or maybe she's the lucky one as I could in no way do any of this if I were being verbally abused...I have my own depression and anxiety issues already. At any rate my mom, who has knee problems, a drop foot, and MS recently fell and broke her wrist. Hospital for a couple of days and now she's in rehab within a NH. OMG...total personality change. She's demanding and arrogant with the staff, orders us around the whole time we're there ( 2 or 3 times a day now for 2 weeks). It's making me so mad at her because of how's she's treating my poor dad. Now we hear she's there until her wrist is healed, no surprise here but my dad is shocked. I am trying to get them to look at their options for living arrangements, one of which is to move in with me and my husband which was rejected out of hand by my mom when I originally brought it up but she's changed her tune now that she's had a facility experience...she thinks the place is awful when in fact it's good. At any rate she's doing that thing with her pain meds with no (diagnosed) dementia...cries in pain over the phone, then gives the care staff the I'm fine answer. Then she's mad she's constipated ( for her that's one day without pooping, those of us on pain meds will tell you how grateful they'd be for twice a week). Luckily I was very vocal when she arrived on our expectations....mainly that despite how it looked on paper they look to me to make most decisions, my dad tips all the aides and dining staff, etc. and that the staff is not vindictive. Bottom line is she wants out, my dad in accurately thinks she's ready to come home. She can't toilet herself yet and he's not strong enough to help her. I told him I was not ready for her to come home, how could he be at half my size and in delicate health? Heck we all sound demented in this description. Bottom line again...there are days I wish I really had the power to make the decisions, and days I want to run away and join the circus. I know what many of you are going through and it's so much worse, it makes me grateful for your support and you have my utmost regard, I know most of your days are 1000 times worse. At any rate I don't get POA general or health for my mom unless my dad can't do it ( and vice Versa) while in reality they mostly defer to me...but not on everything. Oh, I'm an only child with two uninvolved grown daughters. I'm so scared now that they'll gang up on me and refuse to do what they're supposed to...my mom is in defiant mode while my mild mannered dad is threatening to take her home AMA...til I told him the insurance wouldn't cover her stay if they did that...but I'm not even sure that's totally true. The NH case worker suggested I call the Department of Aging and have them evaluated for family care...what this part of Wisconsin calls Medicaid. They won't qualify for awhile but soon, they only have about 50,000$ left. But a fair monthly income...just not enough to cover anything they would find acceptable. Has anyone experienced such evaluations and can you tell me what happens? I apologize both for being long winded and confusing. Have had little sleep since rehab started. Thought it would be a break!