Double use of ATP in relaxing myosin & active transportation of calcium? Is the ATP molecule which is bound to the myosin head for relaxation of the muscle (i.e., to break the cross bridge) also utilized for active transport of calcium to the sarcoplasmic reticulum during muscle relaxation?

ATP is used (hydrolyzed) by ion pumps to transport ions such as calcium against their concentration gradient.

Molecular motors (such as myosin and kinesin) also couple ATP hydrolysis with movement.

However both these processes are separate and just because calcium flux changes happen during muscle contraction doesn't mean that it is the same ATP that drives some kind of a bifuntional enzyme to perform both tasks.

Moreover calcium is released during the contraction phase from the sarcoplasmic reticulum (SR); pumping back the calcium to the SR happens during the repolarization (there is no myosin movement at this stage).