No, although many parents do offer to help pay some of the expenses. Often, the bride and groom pay the expenses themselves, especially when parents paid for a first wedding. The decision is entirely up to the couple and their families.
It's usually best to exclude an ex-spouse (his attendance could upset some of the other guests), but inviting former in-laws is another story. If the groom and his family don't mind their presence, and if the bride and her former in-laws feel comfortable, then it's fine to invite them.