Can anyone answer this for me?

I'll use my self as the example:

I have two kids. I am not, nor was I ever married. I pay child support for my kids. I do not have custody of them. I cohabited with (lived with) the mother for about 3 years and the kids lived with me then but now I never see them. Can she somehow stop me from enlisting? Such as, is there any paperwork she has to sign that she could refuse to sign?

I've tried talking to a couple recruiters but they seem to be either too busy to talk to me or don't seem interested enough to find out. I'm prior service and when they find that out they try to send me to another recruiter.