Mutual exchange

[Sherbertdrops]

Please don’t turn this into a social housing bashing thread, I’m just looking for advice that I can’t seem to get an accurate response for elsewhere.
I live in a tiny 2 bed flat with DC age 9 and 7. Unexpectedly got pregnant with new (and now ex) partner and I’m due in September. I have found a 2 bed house to exchange to, it meets all our needs and it’s opposite my DC school.
The expected move date will be around my due date. If baby comes early will they refuse the house swap due to overcrowding or will baby be disregarded? Will they count baby in the numbers before she is born?
when I have done LHA checks online it says I would be entitled to a 3 bed property when baby is born. I’m not sure if they would refuse the swap on these grounds as baby would share with me until at least a year old. The largest bedroom can be split into 2 bedrooms. I can’t lose this house as it’s perfect for us and the lady who lives there wants my flat due to her disability so I’m nervous about it being turned down and we both lose what we desperately need.
If anyone has been through this or knows the legal side I’d really appreciate hearing from you. Opinions are not necessary. TIA