The IRS doesn't go by custody agreements. It wants a calendar showing which nights were spent at each household, a total and the parent who has 184+ nights for 2012 is the custodial parent. The one who doesn't have 184+ nights is non-custodial.
If he has the nights for 2012, he wins and there is nothing you can do about it. He could sign the form 8332 giving the mother the right to claim the children's exemptions and child tax credit, but this would NOT extend to your return as you are not married to her.
If mom has the most nights for 2012, then she is the custodial parent. However, this doesn't do you any good because they can only be claimed on HER tax return. Unless and until you get married, they can't go on your return.
If you put 4 on your W-4 and you do not have the nights, you blew it. You will owe for 2012. You have less than one month to bump the withholding on your W-4 to avoid the possibility of an estimated tax penalty. (If your withholding in 2012 is more than you paid in 2011, that's fine, but you still have to pay by 4/15/2013.)
Finally, have you claimed these children on ANY of your prior returns? If so, you need to amend. There is no legal or biological relationship between you and them (you never married the mother!), they could only be claimed as "qualifying relatives" if they lived with you the entire year, you supported them and the mother had less than $3800 of income. Since they spent nights with their dad under the custody agreement, they do NOT meet this test. Your fiance might, but the children do not.
Edit, I just figured out that 2/2/5/5 is a notation that says out of every 2 week period, each parent gets 7 days and nights. However, the tax year has 2 extra nights, so even if they hadn't changed the schedule, somebody has the children more.
If either of the parents can claim the children, then you cannot claim the children. You can claim the children only if both parents are unable to claim the children, and you meet all the other requirements. Since you gave no reason why your fiance cannot claim the children, you cannot claim them.
There is nothing that can be filed to "block" a claim until a claim is made.
The only person in the world with the ability to stop his claim is your fiance. If she claims the children, herself, that might do the trick. If only you and he claim the children, and she does not, then your claim will be denied, and his will be allowed, because he is a parent of the children and you are not.
Verbal agreements pertaining to the claiming of children on taxes are not valid. Any transfer of the ability to claim a child must be in writing. Also, the transfer must be from one parent to the other parent; an agreement to let any other person claim the child is not valid.
You don't really need to do anything to "correct" your taxes. You do need to file your taxes without claiming the children. You also need to give your employer a new W-4 listing the correct number of dependents.
There is no legal action that you can take for someone breaking an agreement to break the law. Since it would have been against the law for you to claim the children, you cannot take any action against him for breaking the agreement that you would claim the children.