You are repeating the same information wIthout any substantiation.
Unfortunately, I too am repeating the same replies to you.
Two of the English births seem to indicate that the mother’s name was Hale.
I can’t see a birth for James. Do you have one?
As yet, no death has been found for John Smith who you say is the father.
hi did ann betsy or mary have kids or james think jane married herbert wildgoose and thomas married sarah bridgeman
As mentioned earlier, Jane gives her father as William.
What information do you have about Thomas?
If he is definitely the Thomas in this family, it would be best to purchase a birth certificate of one of the English born children to find out the father’s details and check the mother’s maiden name.
Whilst some trees show Thomas Smith who married Sarah Bridgman in Australia as the son of Jane - others show him as born in Preston.