Is my boyfriend needing more than I can give or is he is just selfish?

I'm into a 2.5 year relationship and recently I started to question the "health" and future of the relationship. There were issues dealing with my partner's unawareness of his actions and how those actions made me feel (seemed like he is selfish).

The part that has me most concerned is about my grown daughter. Since I'm a widow, she is very opinionated and protective over me. She has been clear that I should steer clear of anyone "overtaking me" and instead, should have a companion. Now before you say "it's my life not hers"....I am very independent and refuse to be controlled by another, including my daughter or any romantic partner. Yes I think a "companion" at this point in my life is sufficient which gives me more freedom than living with someone but, part of me isn't sure. I really loved being married to my late husband for almost 30 years and in a perfect world, would be very lucky to get that again but I'm realistic.

My boyfriend is pleading for me to stay. He thinks that his "selfish" behavior is in response to being "shut out" by me sometimes (i.e. no pics of him and I in my home but still have pics of my late husband everywhere - he said he understands having pics of him but expected to see pics of us too; I didn't invite him to certain trips I had visited alone with both of my adult kids out of state but he says he understands but hopes that will change; he was "hurt" when he and I visited my daughter and son and in law because he said he was left out of certain discussions, etc. and he was not welcome to a funeral of a very close family friend - I didn't think having him there was a good idea because my kids were grieving and I know my daughter doesn't feel comfortable with him and he didn't even know the deceased).

He "blames" all of the above on "issues he thinks I have with moving on" rather than on his behavior. He is aware my kids come first no matter what especially since I am a single parent (he is divorced and his kids have both parents).

Perhaps it's because I'm independent or maybe even I am having issues with "moving on" after 12 years of losing my husband, but shouldn't he respect my boundaries and take responsibilities for his own actions.

He wants to see me tomorrow (we haven't been together for several weeks per my request for a break - he complained about that saying he was left alone in silence not knowing what I was thinking, etc.).

When I told him I thought he was egocentric too often he went into a long winded conversation about how much he's done for me even when he wasn't happy necessarily doing it because "he loves me" and loves me.

I do miss his company but just want peace and no aggravation at this point in my life. He says he just wants to be part of my life - and not living together if that doesn't work for me.

What do I do?