The best time for you to work out is in the AM; if you really want to get in shape, the morning is the best time and it will suck, especially if you're not a morning person.
It's better to work atleast 2 days in a row or else the work out you did a 2 days ago will go to waste; your body is adjusting to the exercise, so one day of rest after one day of work out will be pointless.
For your work out routine, work out both every day; you have a hectic schedule and it's more efficient for you to work out both every day at the same time. There are tons of core work outs to get you in shape, the most basic being abdomen work outs.
One work out:
Laying leg lifts/ alternating leg lifts
--swimmers do this to work out their thighs and abdomen; you support the body with this muscle.
--atleast 6 inches off of the floor, head down, and arms to your side on the floor. Lift up to a 90 degree, and lower; do it slowly because youre toning and shaping; rushing is pointless and you put more effort forth with less results.
--doing those with alternating scissor legs, pointed/flat feet pointing at an outward angle--much like a ballet dancers 1st position-- will tone your thighs, calves, and your inner thighs, and they hurt like he** when you keep doing them.
--One more type is a circular motion. You do leg lifts from starting position at 6inches off the floor or at the 90 degree angle. Lower or lift your legs, depending on what position, and then bend them and shoot them straight back out or vice versa; alternating directions is great and tones well.
This also works out your lower abdomen and if you lift your head looking up at the ceiling it will work out some more of your upper abdomen; be careful with that because it can strain your neck--the minute your neck hurts put your head back down.
When you're done with atleast 20 reps or more of each type--normal, scissor, pointed, flat, and circular-- bring your knees to your chest for 30 seconds, turn around and lay flat on your tummy and then and stretch your abs by pushing upward and bringing your upper body off the ground with your lower still laying flat on the ground.
Make sure you stretch; you don't want to build bulk.
Check out youtube as well; they have these work outs, I believe; I wouldn't be surprised if they did.