$1100 for a clutch repair...
Your argument is one of economics.
Assuming the car is paid for, an $1100 repair translates to $91 dollars per month over the course of a year. Something tells me that you could afford that. Offer to pay them $100 per month to keep the car and that you want to pay for the repair. Even if the car is not paid for, add that $91 bucks to your current payment and it is undoubtably lower than a lot of monthly car payments.
If you trade the car in, I guarantee you that the depreciation on the car is much worse than $1100. So, you'll be losing money not once, but twice. $1100 to fix the car plus the amount of depreciation. By unloading the car, you and your parents could be losing as much as $3000. So, it's not hard to see the logic in keeping the car.
The most economical solution is to keep the car, get some more practice with the manual tranny.
Quick tips on practice (you can do this on your own). When you get the car back, find a parking lot and just start and stop. Maybe shift into 2nd gear, but focus (pardon the pun) on starting and stopping. What you are trying to do is instill muscle memory. I would guess that right now, you are concentrating on "Clutch in, gas, ease out on the clutch - STALL" or "Clutch in, gas, ease out on the clutch - what the hell is that smell!?!?!?!"
In a parking lot, there are no hills, no traffic, no other distractions to get you flustered.
Another thing you can do and I would be shocked if your parents said no is enroll in the Street Survival Program that is sponsored by a number of car clubs aroud the country. It will teach you more about how to drive the manual tranny and car control than you would ever get from the public system or from your parents.
Check out the web site:
http://www.streetsurvival.org/streetsurvival/
It's a great program. I'm an instructor in the Northern VA area and it is the best $60 you'll ever spend.
Good luck and keep us posted on how it goes.