You are a couple, you live together and you have gone part time with his knowledge and pre-agreement? When this decision was made, surely finances were discussed, who did you both think was going to supplement your much reduced income to cover your bills? You must have done the maths and realised the situation, what did he say at that time.
Who pays the rent and bills, how is it split? As a family you can't afford to move but he is bragging about this investments for the future (presumably in his name) whilst you are in increasing debt? Am I also wrong in thinking the rent is in your name only? It sounds a bit manipulative to me.
Part of me thinks it sounds like you were struggling looking after your child whilst working full time and its not his kid. But then part of me says that if you are living together as a family unit, it does not bode well for the future that he does not see this as a joint financial responsibility and then if it alleviates your partner from certain duties (housework and dog walking), this is a benefit to him that you are paying for by losing your part of your income???
When I first moved in with my partner (now husband), we opened a joint account and each put money in there each month to cover stuff. He was on a much higher income than me. So we added up our combined income, confirmed what percentage was contributed by him, so say we earned £100,000 between us, he earned £70K and me £30K (income can be for paid work, maintenance. benefit etc) , he paid 70% of our living expenses and I paid 30% in line with our income. So say our living expenses (rent, utilities, food, present fund, holiday fund, insurances etc) came to £2k per month, he put £1400 (70%) in the joint account and I put in £600 (30%).
For those saying he owes her nothing - I beg to differ. Once you make the decision to move in together, when a child is included in that family unit, that new adult must take on a parental role, if they doesn't you shouldn't be with them, as the child's welfare is paramount and this includes financial responsibility.
If you were a single parent, and had to go part time due to your child's struggles, you would get benefit (depending on your income) and presumably your partners income would rule this out.
Despite all of the above, if it was genuinely a mutual decision for you to go part time, then his contribution to the household finances should have increased. I'm sorry but he is not coming across as a man I would want to marry if he sees him self financially independent of you and your child.