My last two horses were put to sleep by lethal injection, administered by an experienced horse vet. There was no stress or fuss - it went smoothly and quickly, and the end was peaceful for them. This is the method I personally would always use when the time comes.
You can't please everybody, so you might as well please yourself - and if that involves a fall-out with your sister, then so be it. Also, think the previously mentioned idea of not leaving your tack at the yard should work.
My suggestion is to keep your pony in a large stable, preferably with rubber matting, and have two-thirds of the floor space covered with bedding. I would feed hay on the clean bare rubber mat area. This is what I do with my horses/pony to ensure that they feed from a natural position, and...
I would only leave a grazing muzzle on for a limited time period eg. 2 hours daily. At least this would restrict the amount of grass consumed in that time. My pony always looked unhappy and frustrated when wearing one, so I just use electric fencing to reduce grazing intake now. When a...