Should I try to get my mom to fire our maid?
Yikes! Why would you want to have the maid fired?
Because the maid cries too much every time my mom checks up on her
Work arrangements don't always work out. If you need to fire someone you should do it yourself. You'll look cowardly if you have to rely on someone to always do something difficult for you.
My mom has a much better way with people so the maid will feel better. My mom is good at convincing people to do what she wants.
Look, if the only reason you want her fired is because she cries, then I think removing yourself from the situation is best. No one needs to be fired, and your parents won't resent you for trying to get someone fired for a petty reason.