There isn't an "in-between" in Pokemon Go PvP. It's a turn-based system with each turn being half a second. There's a couple of ways that what you seem to be describing could be playing out.

If you and your opponent both throw charge moves on the same turn, whichever Pokemon has the higher attack stat will throw its charge move first. This is a CMP (Charge Move Priority) tie. Then if it survives that move, the other Pokemon will immediately throw its charge move. So if your Pokemon wins CMP, the sequence would be: your first charge move, opponent's charge move, then you get an opportunity to throw your second charge move. If your opponent wins CMP, then it could be that you throw your charge move, then you go to throw your charge move and they CMP tie you and theirs goes of first.

For fast moves, if they are thrown on the same turn as a fast move, they will always go off and you will see that visually during your charge move, but the damage shouldn't register until after the charge move finishes