Stop sleeping with her now. From the sounds of it she wants to move back to Poland at some time anyway; if she does that with your child, you'll be thrown into the hellfire that is the Polish family court system.
She sure gives a lot of ultimatums..engagement ring-marriage-etc-kids .. : (
Everytime you are here it is because she is calling the tune in a rather abusive and manipulative way (she must be a real knock out)
Even if you say "yes" -Drag her to marriage/couples counseling before you have a kid with her... ! and if she waffles-make it a Priest couselor! they have them! In fact go to one even without her. It will give you better standing if all goes south.
If you are in States I advise you file first! A lot easier to drop it than to be the one with the leftovers.
I can see where she could have some concern, if you had an understanding "wait a couple years then kids" when you got married and the time is expired. We fems do have a quicker "stay fresh " date in reproduction and you have been together seven years (+/-) .... are you guys in your 30s or something? but honestly dude."by July or else"?
And her former demands about having to be married and all... you can already see her morality/Catholic mores are when they suit her (and that goes for her brother's religious mores as well since he is not urging her to NOT accompany him) Because otherwise she would not be even talking about leaving you when you are a good provider and obviously mellow guy.
This type of gal ,as your posts are painting her; is very commonly seen in base housing (US mil). If she gets pregnant? She'll leave you anyway and GOUGE you for support.
Her behavior has little to do with just being Polish or pseudo catholic (practising catholic that need a lot more practise)