Who gets the tax credit is subject to negotiation as long as only one of you claims it. If she wants it that bad and will give up child support to get it, well, most men would be delighted with that. In CA where I practice we distinguish between physical and legal custody. You can have equal legal custody which means each parent gets to participate in major decisions about the children no matter what the physical custody works out to. Check with an OR lawyer to see if a similiar distinction is made there.
Decision-making is dependent on custody. If custody is joint - decision making is shared. Otherwise the parent granted sole legal custody has the right to make most parenting decisions. We should talk to see if a custody modification is appropriate.
Kramer & Associates