What to do if my fiancee’s job is demanding that she not take a second job?

Two different issues here:
1) FMLA and working: you get FMLA leave when you *can't* work (to oversimplify) due to some medical reason or need: if you are working at another job, you are not eligible for FMLA--you can't work while being on FMLA leave because you need to be unable to work to be eligible for FMLA. Taking another job is inconsistent with being eligible for Family and MEDICAL Leave. So if she can take another job while on FMLA, she did not need FMLA and they do not need to honor the protection it gives her for her job.
2) Whether she is entitled to an accommodation. That depends on whether the requested accommodation is "reasonable" under the facts of her job. If she is, say, a payroll or accounting clerk, it most likely is: it doesn't matter too much whether such a person starts at 8:30 or 9:00 or 9:30 as long as they get the job done. But forsome jobs, you must be there on time to do them, like receptionist or clerk/cashier in a retail store or customer service--you have to be there when the business opens or customers show up, and if you are not, you are simply not doing your job. You say that other people would cover for her, but while that may be reasonable in some cases, it's not in others; if a store needs, for example, two cashiers when the store opens, it's not reasonable to expect the store to have one cashier trying to "cover" two registers. So depending on the employer and her job, coming in a half-hour late may be reasonable or it may not be--and if it is not reasonable, the employer does not have to do it.
If you believe that under the circumstances of your fiance's job, the requested accommodation is a reasonable one but the employer will not grant it, she should contact the federal Equal Employment Opportunity Commission (EEOC) about filing a complaint.