I am very sorry to hear about your situation and for your dentist’s lack of attention/treatment when you notified him of the tooth that was still in your gum tissue. His complete dismissal of your request and telling you to have your wife to pull the tooth are both ridiculous actions on his part and the offer of free care for life is definitely him admitting his mistake. I have a few questions to clarify some details:
When did you finally demand the x-ray?
Why did it take 3 years to get proper treatment?
Did you consent to having a bone graft and implant done to replace the removed piece of tooth?
You say the pain is getting worse. Has the implant/bone graft been removed?
I have to say that I’m not a big fan of suing people, but I think you have an understandable reason to do so in this case. I would normally suggest that you accept the offer for free care, but it sounds like your dentist may no longer be capable of providing quality care. I suggest that you consult a legal professional who is familiar with dental cases to see if they think you have a case.
The legal consultation might not be free, but 3 years of pain and difficulties is a long time so it might be worth doing everything you can to get some reimbursement/compensation. That said, I don’t think you’ll be able to do anything about the failed bone graft/implant (unless you can prove that the surgeon is guilty of malpractice) as those procedures sometimes fail unexpectedly – even if the conditions are ideal.
All in all, it’s definitely time to find a new dentist!