Quote Quoting cbg
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Are the two jobs for the same employer? If so, I think I know what your family member was getting at. He's wrong - even if it's the same employer it's still not illegal, but the employer has to be very careful with overtime rules and other wage issues. But YOU would not be doing anything illegal - any risk would be on the employer, ensuring that he pays you properly.

If the two jobs are for different employers, then your family member is just plain wrong with no "but maybe he meant" to save him. It is in no way illegal for you have two jobs.

Tax is right though, that while it's not illegal it's also not protected. You can work eighteen jobs if you want to and you're not breaking any laws - but if any of those 18 employers sees a conflict of interest or even is just offended by your working for someone else besides him, he is free to fire you and he's not breaking any laws, either.
I think that I am understanding things a little differently. OP is apparently receiving a full time salary to be on call, basically 24/7 at one job, but working for an hourly rate at a second one. While I do not think its illegal, I think that the full time, salary employer, would have a serious problem with it if they knew. I am not sure that the other employer wouldn't have an equal problem with it if they knew that at any moment the employee could clock out and leave.