Jack Russells are very intelligent dogs, I don't see why she needs to re-home it!! as long as the dog gets lots of fuss when new baby arrives there wont be a problem!!
If the dog is not used to living with that cat, you should not trust them together!! they may seem fine for a while but Jack may fancy exercising the cat when you are not around and once a Jack Russell gets it in his mind he wants that cat he may take some stopping
I love Jack Russell, I kept them for many years, head strong little bug gers and if it wants you cat it will have it, he will out smart you!!
Mine used to go to work with me killing rats and I saw my Jack Russell chasing a cat across the top of a silo 20ft up the cat jumped off the top and so did my Jack Russell, they both kept running after they landed, the cat was found dead later in the day!! Bad news!!
And my dogs were brought up with cats and ferrets and would all drink out of the same milk bowl together and would have trusted any of my dogs unreservedly with any child or baby but not a strange cat!!!
But saying all that, all Jack Russells are different!!