Is part of the problem of not having a party due to not having a space to hold it? What about a park?
Do they need more items for baby or for the house? If for the house, call it a house-warming party OPEN HOUSE. If it is at their apartment, people will get the idea that it is a small place and not camp out too long. And why not call it a home warming party if you think "house" is too much? They should register at a department store and put baby items on it as well if they need them.
What about "Meet Baby X" if they need items for the baby?
Some type of "party" should be done if you want people to show support with gifts/money. It can be done very low key and inexpensively. People who know them (they ones who are being invited) will get it if there isn't a full-on expensive party thrown, but will feel respected if there is an attempt to provide refreshments.
Did they not get a baby shower, bridal shower, or wedding gifts? Do they not have a large enough family and friend support system? They deserve a party if they haven't had any of the above (even if everyone doesn't agree with the wedding/baby/living situation). That's my opinion, anyway. :)
Best of luck to you and your mom. More people need to support young couples who are TRYING to make it!