In mobile equipment, usually the shuttle valve (to select the low pressure side of the loop) and the relief valve (to hold minimum charge pressure at say 350 or 400 psi) are in the same block/manifold. Sometimes there is an orifice or flow control to limit flow out any given pump or motor, to balance the cooling flows more evenly, but usually that is done by proper sizing of the relief valve. If the RV is small enough, the pressure rise/flow curve self limts the flow.
If the motor flushing falve is set slightly lower than the pump, there will be some cooling through motor, some remaining charge flow at pump.
Other important functions of the charge pump are to provide pressure for the servo stroker control, to provide positive force holding the pistons against the swash plate as they go past top center and back down, and to provide enough positive pressure (typically 250 to 400 psi) at the inlet side to prevent cavitation.
Check the Sauer, Rexroth, Linde, or other sites for 'how hydrostatic transmissions works' type of circuit pages.
kcj