OP, I realise you might not be reading any more, but maybe your daughter is a red herring her, and the real issue is your relationship.
He is a brand new boyfriend and you've already been disappointed by him, so that already doesn't bode well. A husband of 15 years dropping the ball on a birthday is one thing, but at 4 months, your boyfriend (he is not your DP - partner - yet, surely?) should still have been in the loved-up OTT stage and even then he missed this golden opportunity to wow his new girlfriend?
Secondly, what are YOU giving up for this man?
Where do you live now? Do you own or rent? Is it a council house? You just met this man, and you want to give up your HOUSING security already??? In the gentlest way possible, housing is really scary right now. If this guy lives up to the pretty low standard he has already set, you will want out in a year, but will you be able to get out?
If you are a high earner, and you can rent out your house while live with this guy, then that's fine - you have freedom to test the relationship here, but if, as I suspect, you want to blend finances to reduce your living costs, you're playing a very risky game.
Your daughter's reluctance suggests that she is not as enamoured of this man as she might be. Why is that? Is it because, well, he's a stranger?
Honestly, OP, sit tight. If this guy is a keeper, get married next year and move in with him then. Don't give up your housing security without him committing to you in the very convenient way we already have in law to protect you.