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Thank you for your question.
Preparing the taxes in a number of ways is a good idea, and will allow you to compare which one is more advantageous for both of you. Typically filing jointly is best, XXXXX XXXXX depends on the circumstances. You may even agree between yourselves to file the way that is most advantageous, and then whomever claims the exemptions can pay a portion of that to the other parent.
If you file separately, from the IRS' perspective, it is the parent who had the children the most number of nights during the year that is entitled to claim them. If the children were split equally, the parent with the higher adjusted gross income is generally entitled to claim them. That may help in your negotiations with your wife.
I hope this answers your question. Please let me know if you have any follow-up questions.