You can file separately when you initially file for a year. However, if you file jointly for a year, then you cannot amend to filing separately for that year.
Also, you still might not get any tax return money. For a variety of technical reasons, there is often less money, or no money, when filing separately.
If you, your spouse, and the kids all live together, then either of you can claim the children. Either of you can claim all of the kids or you can each claim one kid. But you can't both claim the same child.
If you can't agree and you both try to claim the same child (or all of them), then the IRS lets whomever makes more money claim the children.