Does my uncle's repeated statement, "She is yours," since her childhood and after her maturity, make the girl my wife Islamically, despite his current refusal for us to marry?

If the guardian says, "I marry you to my daughter," and the man says, "I accept," in the presence of two witnesses, then the marriage is concluded. The marriage is contracted by anything that customarily indicates it, such as "I give you my daughter in marriage." However, if the offer and acceptance were made during the engagement and were not intended as a contract, or if there was an agreement to postpone the contract, then it is not considered a marriage. This refers back to the prevailing custom: if the custom is that it is a promise and not a contract, then it is not a marriage; but if the custom is that it is a contract, then it is a contract. The uncle must be alerted that if what transpired was a contract, then he is not permitted to marry his daughter to anyone else. It appears that what you described is merely a promise of engagement, as a contract requires explicit and clear offer and acceptance with witnesses and in a specific gathering.