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So, are you hesitant because of the shared time that you'll have with the kids?
Or, are you thinking that your bf is over-extended and bearing far more than his fair
share of financial responsibility?
It's quite understandable if you answered, yes to either question as either scenario will have a significant impact on you should you decide to move in with him. Just keep in mind that if you accept living with him; you'll have to accept life with his kids.
Now, if you're up to the challenge without any issues or voicing any complaints, then go for the living together arrangement. But, if you're not entirely comfortable, perhaps that's where the "hesitation" that you mentioned comes in, then you better hold off moving in together... as the saying goes, "when in doubt, don't."
Like iam1butterfly said though, are you hesitant about sharing his time with the kids or about him being overly nice about the situation?
Have you met the kids or spent time with them? If not I would advise getting to know them better before moving in with him. That way they don't feel like you are trying to take their father away. But if you are really serious about each other i would go ahead and move in.
Have you talked to him about this? Have you tried to get to know these kids? Would their mother not let him see them anymore if he refuses to pay support? Has he ever considered going for custody (for his child, not hers)? Is it JUST the money that's the issue, or is it the attention?