I don't know if this has been mentioned yet, but in some cases, cashing a check with "final payment" written on it constitutes your agreement to that. If you haven't cashed it yet, I wouldn't. I would require them to resubmit a check to you without that on it.
I'm so sorry they've betrayed you like this. Unreal.
I hope that this works out very quickly. You have given them an irreplaceable, wonderful gift, and it's like they are expecting you to do this not only out of the goodness of your heart but to pay for it also! Not cool.
So sorry that it went down like this. You are an amazing and inspiring woman and momma.