Do I have to be married in order for my domestic partner to adopt my children? I've asked their father repeatedly to sign off his rights because he hasn't seen them in 5 years. He stated that I have to be married in order for this to be done

In most places you should be married and stable for at least 1 years time before the courts even consider it.

Your partner has to be willing to adopt, and the rights don't officially change over till the adoption is final, that is the only way he can "sign over his rights"

You say "domestic partner" is this a same sex relationship. If so that further complicates things in some states. ( again assuming you are in the US)

A few places will allow a long term relationship without marriage.

But to add to the issue is that even if married, he still has to sign them over, unless he is willing to sign them over for the adoption, it is not likely to happen

Many states will NOT allow a step-parent adoption unless you have been married at least a year.

Some states will not allow for same-sex marriages to adopt, period.

Please let us know where you are located so that we can help you further.