How can I stop my shower turning too hot and too cold?
Is the shower mixer a thermostatic control?

We have a similar set up. The one shower with a non-thermostatic mixer is a bit temperamental, but the other shower with a thermostatic mixer keeps a steady temperature. The former has a single control - left and right for temperature (though mixing), in and out for flow rate. The latter has two controls - one for flow rate and the other for temperature.

The problem with the radiators heating up implies that you haven't got a valve on the radiator feed that prevents the hot water entering the system. I'd get a plumber to check that the system is set up correctly.