Unless part of the settlement represents interest, none of it is taxable to you. He might be asking you (or telling you) to claim it as a distribution from his 401K. Generally, that would be bad for you and, unless the settlement agreement specifically states that you are getting "his 401K" rather than getting back child support, would be incorrect.
Child support payments are not income to the recipient and are not deductible by the payor. If part of the payment is for interest on the past due amount, that part would be income to you.
You should tell him that he is responsible for the taxes.
As indicated by Jon, unless the check was issued to you directly from the fund, you will not receive the 1099R for the distribution. You will not be responsible to pay the tax and there is nothing he can do about it.
Generally if you are awarded a portion of his 401K AND have the option to roll this money into your own plan rather than take the distribution, you should not be taxed.
Based on what you have posted-
You have no obligation to the IRS regarding this money. You received child support that was long overdue but, just because you received it in a lump sum, does not make it taxable. The source of the funds, i.e. his 401K, leads to a tax situation for him, not for you.
Keeping some for emergencies is a good idea. You do not need to reserve any for an IRS payment.
It sounds like the administrator did not properly account for the QDRO either when making the distribution or when preparing the 1099.
Did you get the check from him or from the 401K?
Do you know for sure whether they got the money from him or directly from the 401K?
Did you ever receive notice of an executed QDRO?
Did supportkids receive the QDRO on your behalf?
If this was a QDRO distribution, you had the option of rolling it over into a IRA so that there would be no tax. Granted you may or may not have actually chosen to do that, but you would have had the option and, certainly, you would have had advance knowledge of any potential tax issues.
If the money is taxable to you, for whatever reason, the fee you paid to them should be deductible. If the money is not taxable, the fee will not be deductible.
I will see you through to the end on this if you will keep feeding me the information.
The only other thing I will say for tonight is - if there is some kind of payment from you to him beacuse of this, support kids needs to pay their share. It seems like they dropped the ball somewhere.