Hi OP.
Your mother was a cruel woman. You know that because you would never say that to your child. You are a mother now and have your own little family. You will have friends and colleagues and your baby.
He's obviously gone to great lenghts to promise everything, but now has withdrawn and gets cross when the subject comes up and not just when you mention it. He won't talk about it. I think this points to the fact that he is very unreliable. He may say he wants to be a great father/partner - but he's not showing it. The extensive lenghts he's gone to in the past to plan weddings/rings etc... and then never delivered make him a very untrustworthy person. His promises ( and marriage is essentially a promise) are meaningless and don't stand the test of time.
He seems to have checked out and there is no intimacy. You feel very unloved and rejected. So it makes sense to consider the current relationship as it is now, instead of the previous honeymoon phase.
Currently you are financially independent. You own your own house and you pay all the bills. You have had a beautiful, longed for, baby. All of these are huge positives, the building blocks of a happy lifetime.
You from the sound of it do most of the childcare. Do you have any support from friends/family - if not you should start going to baby groups and making new local friends - What does he do?
He currently lives rent free, bill free - what does he contribute to the upkeep of your child? You said he was going to save for the wedding. What has happened to that account? Does he help with childcare/shopping/coooking/share household chores/plan days out/holidays/ go to family gatherings/plan and celebrate birthdays?
Does he give you the chance to have time to exercise, go to the gym or a class to tone up after the birth? It's quite common to put on weight after the birth if you have no time to yourself and many sleepless nights. But people do recover once the baby gets into a good routine. Who deals with the baby in the night? Is it equally shared?
you haven't reallly mentioned this side of things.. but I would expect that someone who has checked out or is checking out... is not pulling their weight. I could be wrong of course.
Even if he suddenly proposed, I don't think the relationship is in the right place for it at this moment in time, unless he suddening stops being withdrawn and uncommunicative.
Marriagewise, if he gets the talk and then gives in... there's no guarantee that he really wants to long term. All the evidence of his current behaviour is against that . Rent free , bill free and fatherhood without the effort is very attractive in the short term.
You'd be marrying for the wrong reasons and putting yourself at great financial risk - (no risk at all on his part) which would slash your independence in half and make things difficult with parenting. As you' have a child to look after... you now have to take the finance side very very seriously. The child's future is your priority.
I think you need to think very seriously about this. Marriage can be wonderful.. but not if you are married to someone who is not fully invested in it.. it can be a misery.
You are young and could go on to find a more fulfilling relationship.
The best thing you could do at the moment is get some counselling for yourself to talk it through and make some of your own decisions... and then try to get him to communicate. If he won't/doesnt want to...and won't say why he's unwilling to communicate with you, then both you and your child are better off building a life of your own. But talk it through with someone professional in real life, it's a big decision and from the sound of the way your mother treated you, you do need some help to overcome the pain that caused and to realise that you have a right to be treated fairly in any relationship, romantic or otherwise.
I wish you all the best with your decision.