Before you make the move, think about how your kids will take the breakup if it happens.
+1,000
I have a friend who is going through this. He and his lady love (and I like her a lot, she's a peach) moved in together...then found that their joint household was making them both unhappy. He signed a multi-year lease on a house that he wants to be out of before the first year is up, and she might not want to stay there, either. So, they are looking at possibly breaking the lease, plus establishing new households. The only bright side to the whole deal is that their relationship is going to survive the division of households.
That said, you and your girlfriend would be wise to have some very extensive and thorough conversations, just the two of you and all six of you, about how you run your separate households and how the joint household will operate. Also, if you are finding a new residence, find one that either one of you can afford ALONE - even if that means doubling up kids in a bedroom, rather than finding a place that will allow each kid to have a separate bedroom. And if you find a new place that allows YOU to build/furnish a man cave, all the better. (Men need a man cave, it's a biological fact.)