Re: Refinishing Old Radiators vs Rad covers
One time I chipped all the peeling paint off a 20-section radiator with a flat screwdriver and a hammer. The rad was only peeling about 30%, but we knew it would be a repainting nightmare unless it all came off to bare metal. I worked on it for about an hour a day for a week or so, at the end of my regular work on that house (I was there for almost 3 years; big project) Short work periods because the pinging would drive everybody crazy, including me. Impact is a effective way to chip off thick paint.
Radiators can be removed by separating the unions. You could then do the work in another space, or just move your kid while it's ongoing, use proper safety methods (thick plastic sheeting, HEPA vacuum, cleanup with tsp to absorb the lead dust). Unless you take off the elbows and valve and cap the pipes, though, you will lose heat, because the system has to be drained. In warm weather, no problem, you could probably get it all done in one awful 10-hour day.
I primed with a red oxide primer and painted it with some kind of rustoleum, both in rattle-cans. If you have steam heat, then radiator paint or high-heat paint would be advisable.
I went back last year and saw the same rad, no peeling and looks perfect after 13 years.
Remove not the ancient landmark, which your fathers have set.