my partner had 2 children when we met and now we have a baby so i can see the two sides, however it is completely wrong for the FOB to introduce the child to their new partner so soon, i was with my partner for 4 months before i met his children and i met them as their daddy's friend at first, not girlfriend so that there was no pressure on them. i got to know them for a few months and then told them i was their daddy's girlfriend and now we have a 9 month old baby, they have a new little brother and they stay with us 3 times a week and have their own room with us and me and their daddy are together 3 years.
3 weeks is waaaaay to early to meet a new partner, her messaging you is completely immature, unneccesary and wrong. and what she wrote on facebook is ridiculous!
and he is completely wrong to go behind your back, as primary caregiver, you as the child's mother has to know where your child is at all times if you are entrusting someone else with your child, and that includes their father if the two of you are no longer together, so in order to get the respect you deserve as the child's mother, i would get visiting days and times agreed through solicitors and conditions of the visits set out - for example one condition being that you are to be made aware where your child is if he is taking the child anywhere and another condition being that your child is not to be in the company of a new partner until you have met them and given ur ok, and if these conditions or days and times arrangements are broken then he loses his unsupervised visits.
In my case my partner's ex was completely irrational and didnt seem to care what happened with her children as she never once asked to meet me before i met her children, she was just glad to have the children staying out of the house a few times a week, nomatter what but if she had of wanted to meet me i wouldn't of thought twice as its about whats best for the children at the end of the day and children should not be introduced to different new partners willy nilly and that goes for both the mother's new partners and the fathers.
The last thing you should do though is to get into any messaging or facebooking with the new girlfriend as its only going to cause drama!
good luck!