We found that by tieing a scarf or leaving a bag on the buggy it stayed put.
Going back to your original question though I don't think I've ever see a hire double one.
The single ones in March were about 6euros 50cents/day to hire (about £4.00) or there is a means of hiring them for a longer time to allow you to take them out of the parks and back to your hotel, but you have to pay a deposit on the buggy, unfortunately during our stay there was never a CM present who spoke good English and so we couldn't ascertain whether you got the deposit back, or whether you were paying up front for the days you wanted or whether you still needed to pay a daily charge.
This is a good point to mention, we had my 3year old niece with us and the buggy was useful for inside the parks, my 7 year old even cadged a few lifts on the back, but you can't take them out of the parks, you can't even take them from the Disney park into the Studios, or vice versa, so if you're park hopping you get a voucher to rehire that day in the other park after returning the one you have to the park you hired it from.
Also you can't take them into the Village so if you're hoping to spend some time in there again you might need your own.
Hope this helps.