How long does it take a finch egg to hatch out?

You didn't say what type of Finch but generally speaking it should be around 11-14 days. And yes, it is very likely that disturbing them by moving them is the problem. It's their instinct not to bring young into the world if they do not feel it is safe. The relocation made them feel unsafe. She will not get frustrated. They don't think that way. She will just get bored and will eventually abandon the eggs. Then you can pitch them out and go from there.