I don't normally put it in a trolley, I normally use it AS a trolley with the front basket fitted. Not the greatest as the weight can make it heavier to one side than the other, so the balance isn't brilliant, but it works fine. Push it around on its easy-wheels and hold by the seat (still upright). When Mr Houtkop and I are out together we sometimes put one in the trolley and wheel the other around.
I also never leave mine alone if I can help it at all. It comes inside with me, I don't commute with a lock on principle - and haven't been refused access anywhere (yet). In theatres / concert halls it can live in the cloakroom, otherwise it comes in with me. Most people are very accommodating.