Plot bunnies galore!

Ahh, me! Plot bunnies, plot bunnies, plot bunnies! How can one ever finish one story if two million other ideas appear between the ending and the beginning of the first story???
I'm writing a story for school right now (correction: planning a story. I don't get to actually write till 2nd semester), so I kind of have to stick to that one, but I just got a new idea!
When reading Galen and the Gateway to Medicine for our Rome studies, I read a little tidbit which said that thieves would be trained as gladiators. Murderers were simply thrown into the ring.
And then I knew that there was another story waiting to be written.
Who can say no to those wonderful little bunnies? I'm not sure how I'll be able to find time to write two stories, but I will MAKE time! Persephone and Polyphenes need to be given a story (names are pending).
This is my idea:
Persephone's mother is sick because they are without food. Persephone decides to steal to save her mother. It just so happens that the night she goes to this rich man's house to steal his food, he has some sort of heart attack and dies suddenly.  Not knowing this, she crept through his darkened room, and accidentally drops her knife. She can't find it in the darkness and can't risk staying for long. Also, when she had climbed the wall to get into the house, she had cut her hand (getting blood on the knife). Then she gets caught.
When investigators come to the house the next day, they simply put two and two together (healthy man dead + bloody knife in the room + thief who went through that room = murderer). Persephone's friend from childhood, Polyphenes (po-LIH-fuh-knees; he's similar to Gustave in Ever After) tells her that she's to be sent to be a gladiator in a week.
After that, I'm not sure how it'll go. She's definitely going to escape before they throw her into the ring, but she'll be captured again at the end and she'll have to fight the leopard before the book ends.
As for the middle...? I'd appreciate suggestions. I'm considering this idea: she goes to find her father (who either died or left them or was taken away) in hopes that he can help her since he was an orator of some standing; or maybe not.
As of right now, she and Polyphenes are just friends. I don't see a romance happening between them, but you never know.
Suggestions? Criticism?

~

I felt Mother's damp forehead and she moaned. Sighing, I peered out the window, at the house of blank the senator. Why should he have so much money while we starved? He certainly wouldn't miss any.

Persephone, you're not being wise, I told myself. They'd find you out, and then you'd really be in trouble.

But we need it! 

I sighed again. I had to do it.

~