Asking to reattempt research after having a hard time initially
This is somewhat field-dependent, but a lot of undergraduate research is not really for the professor's benefit. If they needed help, they'd enlist graduate students or postdocs. Working with undergrads is more about giving the student a learning experience.

You don't say anything about feedback from your professor, but in any case, I see nothing wrong with asking to work under him again. As for your idea, it's definitely a good idea to run it by your professor before investing much more effort, as he is in a better position to judge whether it's feasible, whether it's been done before, etc.