Towel rail off and all rads remain cold with HW on.
With your check valve in place this is as expected.
If you fit a check valve to t.rail circuit all should be well but t.rail will then only come on with heating.
If you can move the t.rail flow to anywhere between the pump and the 2 diverter valves you would have all year round operation and you would not need the check valve.
On the drawing, into the flow to by-pass is perfect but maybe not in real life.
On the drawing it would be easy to connect down rads to boiler flow, incorporate a zone valve and have seperate control of heat down & heat up.
In real life this may not be practical but it would make your tees fine as they are and no check valve required.
What is happening is that, water flows from tee 2 to tee 1. Some water will take the more complicated route from tee 2, backwards through towel rail, forwards through rads up and back to tee 1. We will call that a(lternate) r(oute)1
With t.rail turned off and no check valve water flows from tee 1 to tee 3 and some will also take the more complicated route, backwards through rads up, forward through rads down and back to tee 3. We will call that ar2
With check valve in place and t.rail on ar1 is operating.
When ar1 is in operation, the check valve opens and therefore is no longer a check valve so ar2 comes into play and shuts the check valve so back to ar1 etc.etc