both had an agreement that each of them would claim one of the children as a dependent

I am not a tax expert, but from other posts from former CPA's I can tell you that dependency is not a choice Someone either qualifies as a dependent for you or not, you can't pick and choose who gets what.

The 6 tests are:
1. Was she a member of my household for all of 2000?
2. What is your relationship to her?
3. Was she a US citizen or resident during 2000?
4. Was she married at any time in 2000?
5. Did you provide more than one half of her total support in 2000?
6. Was her gross income $2800 or more in 2000?


I believe 5 is the important one in your situation. This will determine who can and cant claim what.