@cindyarboleda20 there is no form to fill out for informal marriage. The whole point is that it happens without paperwork. It happens by 2 private actions and one public action,
1. you agree to be married (private)
2. you live togehter as if you are married (private)
3. you tell at least one other person that you are married (public)
If you have filed a married tax return in the past, that will hit all three buttons, since you can't file a married return without agreeing to be married. That means you are married whether you want to be or not.
If you have not filed a married tax return before, then it sounds like you aren't married because you haven't agreed to be married (when you said "and I will be honest most likely plan not to.") Then if you are the person who pays more than half the living expenses and you have at least one qualifying child dependent you can claim, you file as head of household. You can't claim your partner as a dependent if he earned more than $4050, so he would file a separate single tax return. You need to claim at least one dependent to qualify as head of household but either one of you can claim the second child, if they are both your children. Just make sure that each child is only claimed by one of you. In turbotax, the parent who is NOT claiming the child should not even list them in the program, due to potential for confusion.
There's no special reason that claiming him as a dependent one year and not the next year would raise a red flag--it happens all the time. And even if it does the truth is your best defense. The only red flag would be if you filed a married return in the past, which would be a public declaration that you agree to be married. Then, you are stuck with that until you get a real divorce.
