It's funny, because usually in our games there's not much difference between every-day mode and adventure mode. If my players finish a scenerio, they know that they have something to do after that and what to do, so they just carry on with what they have to do... Here are some tips I could think of though:
1. Have the sceneriops connect into one another. Build your stand alones scenerios into a bigger arc or plot. That'll let you players have clear motivation - If they discove the bad guy was part of a bigger plan etc. They won't feel like they're just waiting for the next thing to happen to their characters, they'll try and do thing to discover what's going on and how's everything connected.
2. Generally speaking, unless they have a clear motivation for something to do, playing day-to-day life is rather boring... You need them to either have something personal to do during that time (Like, if someone is trying to ressurct their dead wife, they'll probably want to activley work on that during that time) - Which I usually one-on-one with the relevant player, or to let them free-roam and discover shit that's related to the overall bigger plot or arc during that time (If they found a mysterious omnious item in the Big Bad's lair, they'll want to use their everyday occupation and contacts to find out what it is). They should have something on their mind, "going to work on monday" is usually not very interesting.
3. If there's nothing of interest that could go down between scenerios, I usually use the "fast-forward to interesting event" function. If you want to go into more detail, play out key scenes of their everyday lives, have them describe how they intract with their life and how what they're doing in as much as they want or stuff like that.
Generally, I'd say the "in-between" time should be as long as the players want it to be - and to make it longer you need to have players interested in that in-between time. Also, make the difference between "in-between adventures" time and "adventure" time less clear.