How to pump tire with cap that won't come off
Judging by your description you have two different tubes: one with Presta valve and the other with Schreder valve. Both should have protective plastic caps that should pretty easily come off. It might be possible that cap on the rear wheel valve is stuck so some pliers might help to unscrew it. 

Regarding pumping tires, your floor pump should have adapter for both valve types so you should use one that fits. 

Maybe, if you have pump for only one valve type, you could consider changing your tubes to be of the same type (that matches the pump). Anyway, it is recommended to change tubes because they get porous and leak air (especially if they are too old).