yes, I think you should let them get visa before you go back.
You do not have to mention you cannot go home or whatever. To attend your graduation ceremony is a good excuse, if not, you can always say "to travel in the States and to visit my daughter", which is proper and understandable.
Mail your documents (copies of passport, I-20, I-94) back to your parents. If the I-94 shows you have not left US since your last entry, I do not think the visa officers can figure out. But I think it is a safer and better arrangemen to let them get visa before you go home.
I hear it's easy to get visa this year. Good luck.