You have not provided enough information. However here are some of the issues.
If your ex wife has agreed that you may take the personal exemption deductions for your children, then you will take the exemptions on your income tax return (regardless of whether the boyfriend does too). Your ex-wife could have agreed to grant you the right to take the dependent exemption in a decree of separation/divorce or by way of IRS Form 8332. You may also be able to take the child tax credit.
Otherwise, the issue is somewhat technical and is heavily dependent on the specific facts and circumstances. Are you the custodial parent or is your ex-wife? Does the boyfriend provide support for both your ex-wife and your children, or does your ex-wife have income and does she support the household?
You probably do not need a lawyer for help with the tax problem, but you should consult a local tax professional. Of course if custody, child support or enforcement of a marital decree is an issue, you will need the help of a local family law attorney.
Are you paying for the support of the kids? Did you have an agreement in the divorce as to who would claim the deduction? If you are paying for more than 50 percent of the support and your wife agreed that you could take the deduction, have her complete an sign a Form 8332 releasing the deduction to you.
Any individual seeking legal advice for their own situation should retain their own legal counsel as this response provides information that is general in nature and not specific to any person's unique situation. Circular 230 Disclaimer - Advice given in this response cannot be used to eliminate penalties with the IRS or any other governmental agency.