I claimed both my children on my tax return because we verbally agreed to share the tax break every year so I filed is this legal?

If you agreed "to share the tax break every year" then shouldn't you have claimed one of them? In any event, if each child is claimed by only one of you, then you should not have any problem. Otherwise, you need a written agreement. In the absence of that, the parent who provides a majority of the support gets to claim the dependency exemption.

Usually, whoever files with the children first wins.