Your question about whether to buy a bigger house with him is a red herring. It is a decoy.
The REAL questions you need to ask yourself is as @Heartoverheadheadoverheart states:
How badly on a scale of 1-10 do you want this relationship?
How badly on a scale of 1-10 do you want a baby?
What impact is all of this having on you?
Then ask yourself what you think he would say to these questions. Are your ratings the same as his? Honestly?
From everything you have written, it sounds as if he does not want a baby at all - but he does want a relationship with you. But it sounds as if he doesn't treat you well or cherish you - dismissing your wants, arguing, no effort made on your birthday, no encouragement to develop a close relationship between his dc and dgc and you.
If he genuinely wanted a baby with you, there would be actions and you would both have done something tangible years ago. Instead, you are now trying to think of counterarguments to thet another of his hoop/hurdle is is asking you to jump through
.
If you were happy in your relationship without a baby you would not have posted here in the first place.
If you honestly thought he was committed to having a baby you would not have posted here in the first place.
It sounds that you are shocked, angry, upset, ashamed and guilty with the realisation he has lied and deceived you and not been honest about wanting a baby. I think this is the real issue you need to come to terms with.