Thought I'd take a minute and post my experience on this in the event this might help someone out.
This is in regards to a person in the U.S.
In July my Mom was found incompenent after a mild stroke. She's been sinking into dementia for about 4-5 years (by my clock) and this was the icing on the cake. She is still in complete denial about being ill. So, because she refused a POA of any kind, I needed to go the guardianship route after the hospital found her incompenent. (You can no longer do a POA once a medical professional deems you incompenent.)
The support staff at the hospital told me I had to get an attorney to do guardianship. I suspected the woman was wrong as she was not terribly bright and had, on several occasions, changed what she'd told me and then denied the switch. She gave me papers she'd drawn up with the names of local attornies. I called one. She was wonderful. Very generous in sharing information but informed me that it would be in total $1200-$1400 for her to do the guardianship. I was ill. Money is a big issue these days. Issues like this cause me to flare with anger at my Mom. Everything she does cause things to be more difficult and more expensive and she has no clue.
Well, I went to the web and did some research and it paid off. Then I called my county's probate office. This is the court that handles guardianship and they WERE WONDERFUL!!!. If you are able to problem solve in any way, this is not a complicated process. I got the package, filled it out, send the couple of forms needed off to people, went to the hearing and in less than 1 month had guardianship. It took some legwork and cost me $295, the county's filing fee.
The biggest and most pleasant surprise was dealing with the local probate court and social security office. They were wonderful people. Easy to deal with and helpful. I am so grateful I am not a person who just accepts what someone tells me as it saved me $1000 to do it myself.
If you are in this situation, especially if you are in a rural area, start by calling your local probate court. You may also find out it's much easier than you'd think. (I've been told that if you live in a large urban area, you really do need to consider having an attorney do it as it's not as easy to get the one-on-one council. But I'd still considering trying it myself as you'd be out nothing but your time to at least start the process.)
I don't know about fighting an existing POA. My Mom did not have a POA in place. Once you are declared incompetent you can no longer do that and it falls to someone being made a Guardian.
I'm not an only child but there's no money or estate involved here. Only responsibility. So getting my sibs to sign a piece of paper saying it was all mine was no problem.
Had there been people arguing to be guardian, and one person could not clearly show that they would be a better guardian, the county documents I read indicated they leaned strongly toward a court appointed (non-relation) guardians. Court appointed guardians are very common both for this reason and, more often, because the person doesn't have anyone to stand for them.
But, like I said, this is a very different issue than yours since a POA was not in place. I can see why that could be very expensive to dispute since, at least in theory, it is changing someone's decision that was made specifically to avoid that happening.