The same thing sort of happened to me, that my MIL mentioned to me that she is planning one. Then when I told my mom, she mentioned that she had been thinking of planning one also. I suggested that she get in touch with my MIL to decide whether it would be easier to have one large shower, or have two (one for each side of the family). If they decide on two, I would ask that my personal friends are invited to my side's shower because I have a much smaller family than Hubs. My mom and MIL are both easy to work with people who get along, so I am pretty sure they can figure this out together without me needing to intervene.
When you talk to your SIL, I would explain that your mom is planning one so that could cover everyone to be invited. You might suggest that they just pitch in with the planning with your mom (if they get along). If they insist on throwing a separate shower, let them know that it will probably be very small, as you were already planning on inviting your friends and family to your mom's shower, and people shouldn't be invited to more than one.