Flow can only happen when BOTH heater hoses have openings. That also means it doesn't matter which hose you block. No flow in any part of this circuit means no heat to the core.
Try this... Take a pair of vice-grips or a 'C' clamp and squeeze one of the hoses so that flow stops. If the jaws are too small, sandwich two plates to cover the hose. You can do this in any convenient part of the hose with your new valve closed or open. After the engine warms up, feel both hoses as you check for heat.
With the clamp in place, take a test ride and tell us the result. - Dave