Let’s start with some questions because you were not very clear.
- Are you legally married to your current partner?
- Are the children who live with you your biological children or only the biological children of your partner?
- Does your partner share custody with the other parent? Do the children ever spend time in the other parent’s home?
- What state do you live in?
I get the impression that english is not your first language. If so, that's okay. But your post is not really all that clear. You need to provide better clarity on your specific situation. Meanwhile, here are some facts.
1) If you filed as married filing joint for tax years you were not "legally" married to the other person named on the tax return(s), then the IRS has caught up with you now.
2) If you filed head of household claiming any dependents that you alone were not qualified to claim, the IRS has caught up to you now.
3) If you filed single and claimed dependents that the mother was qualified to claim (weather the mother claimed them or not) then the IRS has caught up to you now.