Mods staying on between play sessions:
This is already possible through several methods. The easiest method is to simply use a mod launcher to set up a modlist. This way, as long as you are launching through the launcher, the mods you have set to load on the list will always be loaded. I'd recommend using one of the launchers available for download here on the MB to be totally safe, but there might be other launchers available elsewhere as well.
Another method is to set up a batch (.bat) file, which is effectively the same thing, but without needing to download anything extra to do so. It's a bit more manual, but it's nothing super tedious.
Turning off mods during the same play session:
This would be a nice quality of life feature, I've even suggested it in the past. However, it seems as though at the current time there's not really a way to do this. Thinking about it more critically, it would also be a waste of effort coding this in when it takes significantly less than a minute to simply close the game and reopen it to achieve the same result.