On Friday we signed and paid on our mortgage refinance in the presence of a notary. Today (Monday) we got a call saying that they made a mistake on our interest rate on the documents and we have to reclose on the house. This is one of multiple things they have messed up along with way so we didn't catch it since practically nothing they have told us has been right.
Is it legal for them to force us to reclose or is the original closing document together with notary and payment legally binding? Also, they say the loan will expire on the 11th and we may not be able to reclose by then since I am due to have a baby in one week. Is it legal for them to drop the whole loan if we cannot reschedule our closing before that date?

Most likely when you signed the documents they included a paper that said you would cooperate with them in correcting any mistakes made during the closing. However they cannot change the terms of the loan. As long as the new closing papers are in agreement with the terms of the mortgage commitment they gave you then yes, it is legal for them to require new paperwork to be signed.

Where the papers you signed, already signed and accepted by the lender ?