You’re right. Your family has undermined you. It would be a huge mistake for you to compete with your brother or the grandma who seem to be “buying” him with indulgence. Spoiling him will only spoil him.
There are two ways to “win” at a tug-of-war. Pull harder than the other side or drop your end of the rope. In this situation, I think you best bet is to do the latter. Stop arguing with the relatives and let them have your son as their guest for now. Go on with your lives. Enjoy having some time off from parenting a teen. Maybe you and your husband can even indulge yourselves by going to some events or out to dinner since you don’t have to worry about working around your son’s schedule and needs.
Your son has no motivation to give up the freedom and indulgence. I’m hopeful that the situation will get old for the relatives. For now, they get to feel superior to you. But will they continue to want your son in their lives, living the high life at their expense, for very long? Unless they have unlimited funds and patience, there is going to come a point where they will have to draw some limits and your son will be rude to them, too. Teenagers often are. At that point, resist the temptation to say “I told you so” and don’t be quick to take him back. That’s the moment when you can negotiate rules for his behavior at home and boundaries with the relatives.
I wish you well.