Two-Year-Olds and Turntables...

A very none politically correct idea is
It may be your grandchild but it is your offspring's child, hence if they wish to visit and have you be relaxed and enjoy it, it is their responsibility to either pay attention to their child or not stay to long.
A visit is meant to be pleasant not unnerving
Having no grandchildren yet I can say this, when I do I may regret it.

Call Dr. Laura. I will save you the call and say that you have failed in parenting. When I was a child NO meant NO!!! A cattle prod might just be the trick though. Maybe a barbed wire or small electric fence might work also.

Fortunately my kids are old enough that they know that to touch my stereo guarantees a serious readjustment of their VTF (especially when they later try to sit).
If I had a baby or toddler to worry about, I'd put something big and/or heavy on top of a tablecloth on top of the tt. Out of sight, out of mind, out of harm's way.
Uru, kudos for bucking the pc trend. In my experience however, even the best-behaved kids are prone to accidents or unprecedented dares. With a deep-four-figure cartridge that no child would recognize as pricey and frangible, for my own peace of mind I'd opt for removing (disguising) the temptation.
Save the cattle prods for cable burn-in, amigos!!
cheers apo

if you do not have access to a man cave, a very tall chest of drawers/dresser works fine.

It's simple.Play a record for the child. Then a CD of the same recording. She will gain an immediate respect for the turntable and leave it alone.