I agree with the above comments as a way to help curb her behaviors, but I think since you can't lift her, you shouldn't be caring for her. She's very active, and she's the kind of child who will need some physical restraint sometimes, and you are very likely to lose your baby if you appropriately care for this toddler in your condition with placenta previa.
Hi,
Toddlers, from my experience, are cute little balls of energy that can be overwhelmingly exhausting, even when you're at your physical best...
Here's a few suggestions:
Get ahold of a baby safety gate(s), put it in front of the stairs to block the entrance(s), or any where unsafe ~ you'll need at least one anyway, since you have a baby on the way...
Distraction is the key, when it comes to the Mom exiting; she needs to drop off the toddler, and quickly leave afterward. Before they arrive, you can have a healthy snack set out, and a project ( age appropriate activities, non toxic finger paints and crayons w/ paper, dough, etc..) set up and ready to go as the distraction. Mom should leave quickly after saying goodbyes, and not linger, this helps the child shift focus to other activities more easily. It might take a few times for the child to get used to the drop off routine, but eventually it will become second nature (normal). Be sure to speak with the Mom about all of this prior to you putting this plan into action, just so that you both can be on the same page, and agree upon it. Keep in mind, it is going to take a little time for her to acclimate to her new surroundings, and become used to you ( instead of just Mommy) giving her directions and setting boundaries...
Create an activity center just for her; Mom can help you w/ this: toddlers love things that roll, jiggle, bounce, have textures, & make noise; get together things like pin wheels, small plastic balls, mega blocks, wind up toys, slinky's, a few things from home that are familiar to her & that she likes to play with. Place the items in a "special area" for just her :) ~ eventually she could even help decorate her place space w/ her own art work!
Being around toddlers can be a challenge, especially because they are just beginning to learning how to speak and understand words, and it takes a lot of patience on the adults part, but I'm sure you'll get the hang of it. Hey, you can think of it this way, now you'll be mentally prepared for what's in store for you in the future!
Take Care and Congratulations on the new baby :)