@Rossi81,
whoa!
too much, way too soon
time to step back on any kind of relationship for you - other than with your children
focus on your children and your life with them
honestly - if you'd asked me 6 months ago I would have told you not to introduce your children to your new girlfriend until you'd been out of the marital home for at least a year. it's not fair to anyone.
you've got a lot to still sort out about the end of your marriage
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let your gf know that she needs to find someplace else to live
you can let her know that you are willing to casually date over the next year but you can't get more serious than that
you really need to take a time out here
counselling may come into play later but first - clear the decks
spend time on your own - get to know life on your own
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rushing / falling into new relationships quickly can be tempting but it's often also a big mess if people leaving relationships haven't taken the time to get comfortable with themselves as a single person
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it seems like you may a person who needs to give themselves time boundaries
i.e. no dating for x period of time
no introducing kids to new romantic interests for x period of time (I generally recommend a year)
no moving in for x period of time
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don't jump the queue