do they have an independant programmer or one that's built into the front of the boiler?
either way the boiler is being told to fire and it only does that by being given a signal. faulty programmer/stat i'd say.
hot water issue suggests diverter valve is on it's way out. they have a wax stat that pushes a shaft onto a switch attached to the end of the diverter valve. This tells the boiler to fire up. When the wax stat is on it's way out, it doesn't make the switch properly, hence why it goes on and off.