I have 2 toddlers and know exactly what you mean.
That’s why I ditched my Thorens and Mag Lev that didn’t get much use because of the situation - instead got the 1200G that is living and breathing in my living room and gets lots of use now due to it’s neat design. I simply close the lid while playing when they run around, lot’s of fun on listening and dancing for them as well. The best feature: I use small load strap to keep the lid locked when not listening so they can’t stick their hands between to touch the tonearm and cartridge, I put the clamp on the other side of the table where they can’t reach - takes me 5 seconds to release it and stow aside the table and I am ready to play vinyl again. The solution is elegant, toddler safe yet a pure good looking hi-fi table :)