Just read this on mumsnet: as hc says, if the person is partially fit, the doctor's fit note should describe that, so job 2 could be a possibility
If she is signed off sick her doctor should have completed a fit note, which should indicate that either she is not fit to do any work at all, or she is fit to do x amount/type of work. If she is fit to work one job but not another, her doctor would have indicated that on her fit note.
"If her doctor has signed her as being unfit to do any work then of course that would include both jobs. She could get into trouble at her second job for coming into work when unfit, and yes her main employer will be likely to question why she needs to be signed off from them if she is fit to work elsewhere."