Wk2-D2 -- I'm on the clock, but no toddlers. After having a few in-game days off. Wonder if this could be because I did a Reset Everything the day before W2-D1? (and also saved the game.) Going to keep playing to see what I get for W2-D3. This might also be because I'm not friends with the parents of the toddlers? I read that might be a cause. I am still Lv1 Amateur Babysitter.
Hmm.. We get to W2-D3 and the game says I have today off?? Not sure I believe that. I wanted to take a screenshot to show that I'm about a little under halfway-ish to leveling up. -- Today (W2-D3) is Leisure Day. That's why I have it off. *Smacking Forehead* Derp.

I do notice that I don't know one of the parents at all. The other parent does show up as an acquaintance - I did meet them at the festival and nice introduction or something like that. I haven't done that with the other parent. *Blush* That still doesn't explain why neither of the toddlers were dropped off yesterday.
Wk2-D4 -- On the clock, but no toddlers again (2nd day of this happening). Not sure what to make of it other than not knowing the parents of one of the toddlers? Or this profession is -that- glitchy. If tomorrow (Wk2-D5) is still no toddlers. I've got a few choices to try as part of troubleshooting.
1. Quit and join profession again.
2. Reset Town/Evict or Move Household and move 'em back in.
3. Add more families with toddlers into town.
4. Befriend the toddlers and their parents, even if need to cheat - Do this as a test if desired.
Wk2-D5 - Third day no toddlers. Added in some pre-made families with toddlers from the library. - freerealestate on totally rocks!!

Not sure if that will help today, but it should for tomorrow. I'm also moving the family, bulldoze the house, replace it and move them back in. I wasn't feeling all that confident that adding families and moving really helped, so I quit the job and was able to join back up again. I'm hoping all of this helps. Quitting and rejoining wiped out my job experience progress, I figured it would. I still have friendships with the toddlers and that counts.

Game says it's getting close to a few days off. So I might not get to see if this all helped till next Monday. And it's Thurs in-game right now.