It seems he fits you in once a week, OP. I don't think thats enough to constitute a relationship, actually. That is the main issue here. I wouldn't date a man who lived with his mother - his mother wasn't ill previously, was she, yet he was living there? & the relationship with his father doesn't sound brilliant.
My brother is a lovely guy in many ways, nice to girlfriends but he lives with our mum - he has longterm girlfriends doesn't run around here and there but there's always an "issue" when it comes to full commitment point. I wish these women would realise, he lives with my mum because he wants to. Its cheaper and convenient for him, they get on well enough, and there's no pressure on him to commit to anything or change his lifestyle. Thats how I see it.
I don't care what the reasons are, where the apron strings haven't been cut I wouldn't go there with a man. Sorry about his DMs illness though. When she passes, the next excuse will be that his dad needs him so he has to be there ie actually living with his dad.
Always strikes me anew. So many women leave relationships, may stay with parents for a bit but are always striving to move on, and out. Yet, same as my brother, I know of men who went back to mummy when their relationship ended and never moved out again. I don't find that dynamic attractive at all. I think you are a convenience for this man OP and besides, he has already told you he's not up for seeing you more than once a week; and you know that if he wanted to make time and space for you, even to see you twice a week, then he would.
Just a case of whether thats enough for you or not. Then again Im a firm believer in women not being so quick to put their eggs in one basket. I wouldn't be taking him as my "main man", the one I hope to have a life relationship with, at all...