When the divorce girl marries with a child, naturally the child or children can be adopted with the bride. Once the adoption takes place naturally the children goes to Gothra of Second Husband.
The ex Husband will always have visiting rights for his children even though the ex wife has remarried.
Man dont disown their kids after a divorce..they still have all legal visiting rights and the new husband is like a "guardian dad" and he doesnt go through legal procedure to legally adopt his wifes kids.
So why should Gotra change?