Can I claim the expense of braces totaling $2581.00 this year, since my ex will be claiming her this year, or do I wait until next year?

[xmasbaby0]

Who paid for the braces?  When you claim a medical expense you can only claim the amount you actually PAID during the tax year--unless you put it all on a credit card.

[Opus 17]

You can take a medical expense deduction for expenses you pay for yourself, your spouse, or your dependent, including your own child who you are not claiming as a dependent due to the special rules for children of divorced or separated parents (it's a special exception to rule that the person must be your dependent to deduct medical expenses.)

You deduct the expenses in the year you actually pay them to the provider, if you pay by a loan or credit card in your name that you promise to pay back later.  So if you paid the provider in 2018, you list the expenses on your 2018 return.  However, because of the high threshold for deducting medical expenses, you may not actually get a benefit.

You can also use an HSA or FSA to pay expenses for a child who is not your dependent due to divorce or separation.  However, if you pay a medical expense with tax-free HSA or FSA money, you can't also take a tax deduction for the same expense.