Do I have legal recourse?

I would definitely see a lawyer to see if you do have any legal recourse. They have already set the precedence for hiring you as the son of another employee--they can't really turn you down based on that reason. So yes, you may indeed have legal recourse. Of course, they might be forced to hire you under legal pressure, but what kind of working conditions will that make for you? It's something you need to consider before pursuing this avenue.

When your dad is your boss, people naturally will think that's why you got and kept the job, no matter how good a worker you really are.

Anyway, it's only illegal for a company to not hire someone for a few specific reasons, such as their sex, religion, etc. In other cases it's really up to the employer. But even when the company really didn't hire someone even for an illegal reason, lawsuits about it are rarely successful because it's so hard to prove this and the employer can usually show other legal reasons why someone wasn't hired (such as they didn't have the right experience, etc.).

Instead of fighting to get this job, get a job where you would not be working for your dad. That will make you look better to future employers, who won't have to wonder whether you're really qualified (which may be the reason why they don't want to hire you now).

No legal recourse at all. And by the way do you mean sub-contractor instead of sub-custodian?

you're only legal recourse other than being happy is to find another job.

maybe not - most employers have a policy of not allowing one family member to supervise another family member

How over-entitled of you! Uh, no, you have no right for them to have to hire you.