May I suggest that the FOUR of you have a sit down and talk about all of this?
His wife may be saying things to stir the pot (can't see why she would but ya never know)
Bring up ALL of your concerns regarding this right there, in front of everyone! This way there is no "he said, she said" "I did NOT say that", etc. Everyone gets the whole story right there, up front. Everyone knows exactly what is ok, what isn't, what's negotiable, what's stead fast.
Let them know you are not OK with your kids growing up without Mommy because of some STD they (they couple) don't have yet. You are NOT ok with being the 24/7 babysitter. They need their Mommy too.
Write down what you want to say, even if it's bullet form, so that you don't forget to cover something. It also helps one organize their thoughts in a more coherent manner.
Let them know, in no uncertain terms, that having an STD is NOT, under any circumstances, OK with you.
I would also recommend reading LovingRadiance's blog. She and her family are going through some very tough times right now & it can be very helpful to see how others work their way through those times.
There are as many ways to do polyamory as there are people practicing it!