Counter not working as expected
Given the restrictions on what you can use, this sounds like a homework problem, so I won't give a full answer. You need to work this out on your own, and then ask a more specific question if you get stuck.

The key concept is that you need to have three operating modes, or "states" for the system overall:


reset
counting
holding


The circuit you show has only a single flip-flop (the cross-coupled NAND gates) as a state variable, which means that there are only two states &mdash; reset and counting. You need to find a way to have a third state, typically by creating a second flip-flop (more NAND gates).

Part of the problem is that your existing FF is also debouncing your switches for you. If you want one of the switches to toggle between two of the states (counting and holding) on its own, you'll have to find a different way to debounce it, which complicates the design quite a bit, given the restrictions you're working under.

I hope this is enough of a hint to get you going.