Hi C.:
I am an orthodontist and a mother of two (5y.o and 3y.o.). So I am going to give you the whole perspective from the professional stand point and as a Mom. I got a long story…
To start I will tell you not to worry about it, and tell that to you mother in law as well. Do not make a big deal out of it.
When a kid comes to my office because the parents need help making the child stop the habit it is usually around 4 years old and older. At that point many things can be done to help (not necessary braces or any appliance), but that will be another subject and you don’t need that info right now.
My 3 year-old used to suck his thumb, he did it constantly, he even took it in an out while eating switching between the thumb and the spoon or fork to eat his food, you can imagine how annoying it was for me (especially with my occupation).
Well my Mom is an orthodontist too and I sucked my thumb until I was 6y.o., and she used to tell me to leave my son alone and that I can make him quit later. I disagreed with her, because what annoyed me the most was when he started to be a toddler I felt it was an additional source of germs and it will increase his chances of getting sick all the time. My husband also used to tell to not worry about it, that I could fix his teeth later.
Then my sister in law (which is a dentist as well) has 2 boys and both of them sucked their thumb, actually the 10y.o. still does, and the 4y.o. doesn’t anymore. She always advised me to me make him quit early so I wouldn’t go through the nightmares that she went through with her oldest. She made her little one stop before he turned 2y.o. What she did was to put on his thumb the nasty flavored nail polish to quit biting the nails, and he didn’t know what was wrong with his thumb, what was going on, he cried for a week and even threw up once, but he quitted for good since then.
So when it was my turn (3 months before turning 2), I was a complete coward and I felt I didn’t have the heart to do it, but my sister in law gave the emotional support and I tried her experiment. I planned to do it on a weekend, because I wanted to be with him day & night at list during the first 3 nights. So I started putting the nail polish Friday afternoon (when he was taking his nap) and he came to me and said that his thumb was sick, so I put some “medicine” on the thumb (the nail polish) to “make the thumb get better” (I felt like the worst Mom ever….) and he even thank me for it (to break my heart more…), that night he cried to sleep, it took him longer to fall sleep, and he cried the following two nights, and kept asking me to more medicine, he even blew air on his thumb to dry “the medicine”. So to make a long story short, he never suck his thumb ever again, he only cried about it during the weekend, and I kept putting the nail polish for the following 2 weeks, to make sure he wouldn’t go back.
So in conclusion the best time to do it is before they turn 2. Because they fully trust you, and they haven’t starter with the terrible 2’s phase, and they are easier to handle. I wouldn’t recommend doing it earlier than 2 y.o. because if they suck their fingers or thumb is because they have a need of suction, and you have to let them satisfy that need. By the age of 2 that need is reduced but they still do it because it is already a habit.
By now other 3 people (friends and patients) have try this approach and worked perfectly for them as well, but remember it has to be 2 or 3 months BEFORE they turn 2.
I also do not recommend making a child quit this habit if there is any unstable situation at home, like parents separating, moving away from relatives or any change that could affect a child emotionally. In those case even if they are older than 4 I tell the parents to wait until everything gets better.
I would like to make also a comment on some of the answers you got:
The palate can deform at any age, even before adult teeth erupt. What makes the difference it is how, how much and with how much force the kid sucks, and also the genetic predisposition to have a malocclusion. Some kids suck their thumb for 10 years and nothing happens to their mouth, some just do it for a year and they get buck teeth. So there are many factors. But if they stop before two you have greater chance of any deformation caused by this habit.
Good luck, I hope my loooong story could help you.