There is no harm in asking both. I did 2 part time contracts, just short of fulltime in total. It is very hard and you can feel pulled in 2 directions. You will always do more work than the full time equivalent with a PT job, so I would be wary of doing 2 jobs that equal a FT as you may end up doing 120%. I would still go for it though if the times are possible, as this sounds like a good school and your future at your present school sounds dodgy.