"have to convince a judge", yes that means you need a lawyer, preferably one the judge likes.
I had to get a lawyer to help me with my dad who had bad dementia, but only in certain respects. He was bad on violent criminal things but was correct in that they would never put a 92 year old in small town Texas jail. Fortunately, I suppose, the DA would never prosecute the stabbings and shotgun events he committed. The sheriff did go after him for crashing into a deputy's car (no license to drive) resulting in a big fine.
Funny thing, my lawyer said he mostly represents the other side of my issue and he had doctors that would say anything he wanted so to be prepared for a long experience.
It was a long and painful and super expensive effort but had to be done. My lawyer is now a district judge, keeping the money flowing to his union.
My advice, never ever involve the state's help with their adult protection folks. That will add a year to your project. And if the one who is mentally deficient, or a 3rd party that is interested, gets a lawyer you are looking at close to two years and $200,000.