I completely agree with Zoollinmyfridge .
This is MN and therefore whatever scenario you present on here with an issue involving a man and a woman... the woman will be the blameless victim and the man, someone who is one degree removed from the devil himself.
Personally, I would find someone willing to go through a pregnancy with a bloke they had slept with a couple of times - someone with an agenda. !
Either to have a baby at all costs (does she have children already ?) or someone looking for a 'good bet' in the shape of your DH and his income.
(Here I presume he earns well and she not so well ? )
Contacting the family - for me would be the biggest indicator of someone who had planned for a baby to bind her to your husband - and thought this would be the route in - when that backfired.
Would I be backing off in your situation? No way. Not if I wanted to make my marriage work. Her plan has been to make sure you two separate . I would not playing into this scheme.
I would also not be working myself into a frenzy about how your children feel about the situation. They will take their cues from you. Children of 9 & 6 have no understanding of the emotional angst involved in these situations - unless you express that angst to them. The baby isn't born yet. What's the betting that the baby's mother will not even allow visitation unless your DH agrees to her conditions - which will no doubt involve some kind of pretend 'happy families'.. visits to his family with the baby etc. ? As for allowing your DH to bring his child home - without her in tow.. I doubt it. Not without a court order. So if I were you I would start the conversation with your kids a few months after baby is born based on how the land is lying.
You need to make a decision. In or out. If you walk away then no one will blame you ..
BUT if you decide to stay ,you need to get off the back foot and start laying down the law of how things will be going forward.
No 1. DNA test. This has scam written all over it. Contrary to MN folklore, accidental pregnancy by someone using contraception correctly is extremely rare. What is not rare - is people lying for their own manipulations .
- Visits . Regular and brief in a public place if child is breastfed. If not breastfed then baby handed over to father for regular contact. (Will probably need a CAO for this as will not happen voluntarily)
3 ALL communication to be via email that you also have access to. All communication to be baby related. Anything not baby related to be ignored. - effectively , if he wants your marriage to work and for you to stay he must agree to absolutely no ongoing relationship of any kind with the mother. Only the child.
If he can't agree to this then I would walk and leave him in the pile of shit of his own making.