If your father in law has purchased the piece of land in the year 1989 or 89 then upon his death how did your mother in law became an absolute owner of that property?
(i) Is the gift deed executed by mother-in-law valid? With this gift deed, is my wife the sole title holder of the land? Can she dispose the land alone if she wants?
If the property transferred by executing a gift deed in your wife's favor was on the name of your mother in law or if the property was purchased on her name or it was bequeathed in her favor by your your father in law, she becomes an absolute owner of the property and has a marketable title so the registered gift deed can be held legally valid and cannot be revoked, but if the property remained in your father in law's name and was an intestate property, then the gift deed insofar as the share of other legal heirs of your father in law is concerned, becomes invalid, therefore your wife cannot be a sole owner, she will be entitled to only 1/4th share in it.
(ii) My wife wants to dispose the land given to her on the basis of the gift deed. Purchasers are asking signature of my elder brother-in-law also. But he wants equal share on that. What should my wife do to sell the land to?
If the above answer is understood, the present question stands answered accordingly. Your wife has to ascertain the facts and legal validity of the gift deed.
(iii) If the mutation done by my elder brother-in-law is correct, then what should my wife do to get her share. My brother-in-laws have managed relinquishment of my co-brother son and trying to sell the property without my wife’s signature. Is it legally possible? What should my wife do to get the legal benefit?
The Mutation done by your brother in law is also not valid. If the property remained intestate property after your father in law's death,then that will now devolve upon all four legal heirs, i.e., on two sons, your wife and the legal heir of your deceased sister in law. Therefore your wife can fight accordingly.