I have been recently divorced and it can be such a hard thing for children
Divorce IS hard.  Annulments, declaring marriages null and void are so much better.  I, too, am divorced.
I have heard about annulments but don't know much about it. Isn't there a time period where you can file?
Yes, but I'm not sure how long.  Divorce isn't allowed in Vatican City or in the Phillipines.  Only annulments.