bookdreamer It seems that the sponsoring is being taken care of if I understand correctly, but I would advise you work with an immigration lawyer in the States to look at the nitty-gritty and financial aspects, which can be considerable. Face to face with someone at the American Embassy in London re. you situation is something I would also do. Make sure you get the right department. Meanwhile, perhaps your son-in-law will be able to look at this from the Texan law perspective and connect you to the appropriate people.
This may well be a long process, but getting it right is imperative.
Health insurance is a minefield out there - so I hope your son-in-law's insurance covers all possible future health issues you may have.