Runner---need HELP with core.

2007nuna

I've been a runner for a while. I try to vary my running routine and route but I still feel as if I've hit a plateau. I really need to work out my core but I'm not sure how to go about this. Right now I run 3-5 days a week so I need to incorporate core strengthening without compromising fat burning. I'm still trying to lose weight.

My plan is:
1- join a zumba/pilates studio and go once or twice a week.
2- continue to jog the other days
3- add core exercises at home too

What is the best way to do this?

I looked online and found some calisthenic routines and some using light weights (sit ups/push ups/squats/lunges/planks with a ball). Here is a link: http://www.runnersworld.com/article/0,7120,s6-238-263-266-12756-0,00.html
They look like routines that would take 20-30 minutes to complete. Is this a good way to do some core training at home?

SO HERE IS MY DILEMMA:
Should I do those alone on days I don't go to class or jog?
Should I do them before or after running? If so, do I then shorten my route on those days?
Should I do them in the morning and run in the evening or vice versa?

Keep in mind I am a mom of two and work full time so I don't have 2 hours at once to work out. I really want to make it easy to fit into my schedule.