Bride-to-be and groom-to-be are pretty much commonly used. My question is can we say father-in-law to be or mother-in-law to be? Or if that's not correct, what do we say here?
You can say this, but there are better alternatives. It would need all the hyphens (so, "father-in-law-to-be") but I don't like it. I'd just say "future father-in-law".
If you jilt the bride-to-be or groom-to-be at the altar you can even say ex-father-in-law-to-be(!)