So she wants to be in a "V" configuration and you want to be in a "triad." You will have to ask him what he wants to be in, if he even wants to be in polyship at all with you.
The biggest question I have is how does these sorts of relationships affect children.
IME, the kids themselves don't seem to care. They are very accepting. Where they get affected is how OTHER people react (ex: grandparents) or in time management if there's too much shooshing them around and not enough family time.
And that's me watching friends and their kids. For myself, I skip that whole bit in favor of Closing and parenting with DH without any poly relationships happening.
And at what point In the relationship do you go public?
That's up to you and the other polyship people. Each has a different comfort level.
Perhaps resources would help you: