Myhusband spent most of last year leaving and coming back, leaving and coming back. We officially separated near the end of the year. I gave my children's biological father permission to claim them this year. He filed and it bounced back that the kids had already been claimed. Is it legal for my soon to be ex to claim MY children on his return without my permission, or signature?

Not unless he was providing more than half of their total support.

Have the biological father file the return by mail, and the IRS will determine WHO is allowed to claim the children.

Please clear something up - did you and your "soon to be ex" each file as Married Filing Separately? And who actually provided financial support for your children?

If you are the custodial parent you should provide the father a signed IRS Form 8332 - this is required for him to submit with his return since he is not the custodial parent.