Like, I’m the sperm donor, not the one who carried them for nine months.
Neither of my moms birthed us and that doesn’t make them any less of moms. And we don’t even talk to the person who birthed us (we probably have talked to our formally anonymous sperm donor more recently and are on better terms with him). You shouldn’t let irrelevant things make you feel like you are less of a mom. If its a compromise for your children, that seems like a good enough reason to accept “dad”, but you shouldn’t feel like you would be an imposter (or you should at least realize those feelings aren’t rational).