I agree with some others thoughts above, that this is not so much an issue of how to out a rude roommate, as it is of caring for an older parent who is now in a disadvantaged position. Especially in this case, as I read points 1-6 above, I don't think those should be brushed aside or minimized. The op says in her points starts off by saying how wonderful her mom has been to her, and she was given everything her parents could give to her, and then even goes beyond this by helping her raise her son when she was apparently single.
I think that if this was just some college buddy who was partying, not paying rent for shared due etc that would be a diferent t issue. But this is very different, this is her mom, who she writes was a wonderful generous parent, that she was given everything growing up and had a wonderful childhood. In addition, her mom did something that not all grandparents do was help raise her son. I'm assuming this was very good care she provided or else she would have had someone else watch him, or daycare,etc.
there are options like hiring someone thru an agency (usually expensive and can't really compare to the personalized care of a loving grandparent, there are also daycare centers ,again expensive, not at all the one to one care of a grandma or grandpa), and for at least part of the time she did this if I understand the bullet point, grandma was living almost an hour away which in my mind makes it more of a sacrifice on gmas part.
I think bc of these things its realy important to take a step back and look more in depth at some issues and how to resolve them rather than just quickly tossing her out. That would be the quick amswer, but may not be the best answer. also as one poster pointed out, even if she does manage to get her mom moved out, it may not be that simple , she might be needed to provide some type of assistance or care to her.
Her mom according to everything I see above, was there for her when she needed her, and it would only be right imo to at least first look at maybe how the living situation can be made more doable, rather than just taking the quick way out. Here are a few things I think should be thoughtfully considered and then discussed in the context of "how can we help her, "rather than just how can we oust her.
There was mention of how the op felt her mom hasn't been responsible with money her husband left for her. Rather than just assuming that's all there is to it, I see a couple underlying issues with this...at least one other poster above wrote how it sounds possible her mother might have depression which could explain why her mom who was so nice her entire life, is suddenly cranky and critical. I wouldn't overlook the impact her husbands death may play into all of this..the other issue with this is how does the op really know she's been irresponsible or how much money the husband left her? Did she sit down and show her a paper with how much he left her, etc or is this more an assumption? Please note Obviously I'm not saying either way since I don't know. But I am just raising the possibility she might have thought her dad left more than he did.
It says that her main reason for wanting her to move out is bc she's irritable and critical. I'm not trying to excuse this behavior,but in older adults especially if they are widowed and like her mom, this is not characeteristic of how she was all those years......there is a high incidence of depression, and this is a symptom of it. Again I am not saying this is the case, but from what the op writes, this wasn't a part of her moms character in all the years , it sounds like amore recent thing. In looking at how to help her, what about having her evaluated to see if she may be suffering from something like depression. I'm not saying this is the case, but given her age and the fact this is not how she was during her life, and that she is widowed,, it wouldn't hurt to at least have her evaluated to see if there is a depression or some other related issue. Beyond just a simple evaluation, it ight really help her to be able to talk with a counselor, I think this would be helpful for anyone who's lost their spouse. In fact a counseling session for you and your mom together might be helpful in gaining understanding of what the real issues are. It sounds like she spent most of her life caring for others, this is a issue for women when they get older feel a loss of what their role is .
To kind of summarize this, I think the fact that the op describes her mom as a woman who has been a kind and giving person thru her life, helping to raise her son, etc , the recent behavior of her being critical and irritable should be considered as a possibility she has depression or other related condition. This is kind of a red flag esp in older adults and if they've lost a spouse, it becomes even more of an indication. It might be a good idea to ask if she'd be willing to be evaluated. Offering to fnd resources for counseling or support group f widows might be all she needs to start pulling out of this if it is a life change type of depression. I know somene who's mom still has grief and depression from the loss of her father that happened way back in 1999. Grief can hold on and affect a person, especially with the major losses such as parent or spouse.
I would try to look at this as what is causing this recent change of behavior in her mom and look at how to help her with that, as a starting point. If it is depression related to major loss, grief, getting older etc it could be that medication and counseling or whatever treatment she gets could resolve the issue of her acting irritable