I say stay for the time being. With the twins coming I'm sure they would spend more time in your room anyway, you could always get one of those playpen combo thingy's that both babies could fit in to sleep. It had great storage space also! Either way I think you should make it work so less stress on you, hubby, which means less stress on all the kids!
Your kids are still very young, i dont think they will mind the crowded space. If you love the apartment stay. You can take the time to save money and when the kids are a bit older you can move to a bigger place. The last thing you need is extra expense in rent with 2 babies on its way.
If you can afford it then I say move. It might be a little tight with 4 kids under 4.