I couldn't find anything about deducting, from US taxes, legal fees for collecting child support. My opinion is that they probably aren't deductible because only legal fees incurred or paid for the production or collection of taxable income may be deductible. (You may deduct legal fees for collecting alimony because alimony is taxable income. These deductions are taken on line 22 of Form 1040, Schedule A, Itemized Deductions.) Child support isn't taxable, so the IRS apparently isn't going to give deductions for someone's efforts to increase those amounts.
--Seasons (not in a blended family, but this info is relevant to me as a single parent)
The only thing you owe to others is to behave with integrity.