Carol;
This can be done, but Old Army Pass and New Army Pass cross the same divide and are simply alternates that are very close together. You can do Whitney from Horseshoe Meadow by going up Rock Creek past Sky Blue Lake, crossing what is sometimes called Crabtree Pass, descending to a lake below, then ascending Discovery Pinnacle and joining the Main Trail near Trail Crest. It's a fairly long route and it makes sense to descend via the Main Whitney Trail, as there is no loop as such. The route back otherwise is simply back-tracking. Pick up a copy of R.J. Secors' book "The High Sierra, peaks, passes, and trails"
It will provide details that are clearer than what I've just described.