How do I convince my parents to let me buy this saddle?

Since the problem is the source, not the saddle, I'd show her that the cost of the saddle over the internet, with delivery both ways, is less than the cost at the local place. If it's not, buy it at the local place.

One word about the saddle, though... make sure you get the same size tree and the same size seat! Even then, it won't fit the same, because the stable's saddle's beyond "broken in" and approaching "broken."

If it's the exact same saddle you ride in at the barn, it's unlikely you'll need to ship it back since you already know it fits you, fits the horse, and suits your tastes. Tell her that. Volunteer to pay any shipping costs associated with shipping it back if you do have to do so. Show her that you have all of the money for the purchase of the saddle as well as enough left over for return shipping if necessary, and show her that she doesn't have to spend a dime.

My family and I have bought many things over the internet (several western show tops, two western show saddles, my show chaps, my English saddle, a couple of other English saddles over the years, various other pieces of tack, English clothing, boots, etc.). Except for the occasional return on clothing items when they didn't fit (there isn't a tack shop near here to try on), I've always had great success with the process...no lost items or anything like that.

Well you just tried to sell the idea to us.. so do the same to them... but make sure you are not just trying to buy it on impulse.. maybe there might be one just like the one online at the cheaper tack store. that way you will have your saddle and your parents will feel like you listened to them. its a win win. Your parents might have a point and if for any reason you buy online and its not what you expected, having your parents retune it will open up weeks of "I told you so"

Being a parent, I can kind of see your parents way of thinking. It would all depend with me who you are doing business with online. Ebay, nah I wouldn't risk it. A reputable dealer with catalogs, etc., they are fine and will accept returns. If you are dealing with a used tack dealer, be very careful. Only one I recommend (but I am sure there are others that are just fine) is Middleburg Tack Exchange. They are wonderful to deal with. Good luck, and give your parents a break, they are older, have been there, done that, sort of thinking!

Convince them by telling them the health benefits you recieve ,if they allow the saddle that you wish .

Tell them the same thing you just said in your question.

Get it. Say "last time i promise" and just list everything you do for them and how go you are of a kid. lol GOOD LUCK!