Firstly let me say thank you very very much for all the help.
Interestingly enough I intended to buy some boost circuits and hit the wrong link and ended up buying 10 step down circuits. When switched over to vape mode the parallel positive path would be broken, leaving only the series path going through the switch, and when in charging mode the batteries would only be connected to the charging board as a parallel connection.
To be clear, the diagram shows the two battery negatives connected at all times. That is a problem in a circuit where the batteries need to be in series when in use.
It looks as if the positives are connected at all times as well, on one side of the switch, with the other side of the switch connected to the charger. This would also be a problem.
The charger should also be isolated when in vape mode.
The batteries cannot have those extra connections when the batteries are put back in series. The only way I see to meet all of those conditions is to have
all four individual charge connections opened by separate (possibly ganged) switches when in vape mode, and those need to be opened
before the batteries are put back in series.
While I'm not an electronics engineer, I was a certified electronics technician with over a thousand hours of electronics theory training, and I can say with certainty that the above circuit is unsafe, and will not work. This is why I said earlier that it is not a realistically buildable circuit. It can be done, but it'll need to be well more complicated than that, to be done correctly.
I'd advise charging the batteries individually, as retird said.
If you went with a boost circuit, this becomes a rather easy problem. Just isolate the battery from the boost circuit while charging.