You are facing a dilemma that doesn’t have a perfect answer but we may be able to offer some useful information. For your current situation, you can take photos and present them to the judge to show why your child was not in a safety seat. You may be able to appeal one traffic fine this way.
As to whether or not the method you are using is unsafe, studies haven’t been done to prove or disprove the safety of various restraint methods for children in spica casts. And those casts come in several different arrangements.
There is the two-legged (goes down both legs) version. There is also a one-legged spica cast and a one and a half-legged (covers one leg down to the toes but only goes down to just above the knee on the other side) spica cast. Some children are placed in a semi-flexed position (for hip fractures) while others are straight-legged.
There is a commercially available special car seat for smaller children in a flexec spica cast and a chest restraint system for larger children. The children in the middle sizes fall through the cracks. Some parents arrange for ambulance transport. The child is strapped on a flat bed, which is tied down inside the ambulance. It’s a very safe way to travel but unless your insurance company covers the cost ($500 to 600 per trip), it can be an expensive way to travel.
Some hospitals keep some of the special car seats on hand and have a loaner program. Others will refer you to a rental company. If neither of these exists in your area, then travel becomes prohibitive.