Re core exercises, this is a recent post which gives a few basic exercises:viewtopic.php?f=5&t=5150
I also found this from the MSTrust which gives more exercises:http://www.therapistsinms.org.uk/downlo ... update.pdf
There's one exercise where you are on all fours on the floor and you raise the opposite arm and leg - my physio said you can eventually get so that you can raise the arm and leg on the same side of your body - I still don't know if she was joking or not!
For balancing, stand in front of a full length mirror, feet together, and try to stand on one leg, keeping the side of your body which is bearing the weight absolutely upright. If this is easy, make yourself more unstable by moving the raised leg sideways, forwards and backwards.