A couple more issues I've run into:
Sometimes if the toddler bed is pushed up against a wall, the parent will act like they can't get to the bed. It seems like they pre-choose a side, and then cancel if they can't reach the side they chose. It seems like which side they pick initially is random. But after that, they always pick that side. So once they decide they can't reach the bed (because the side they chose is against a wall), they always say they can't reach it, no matter how many times you try. Moving the bed away from the wall, or even pushing it up against the opposite wall, so that the previously blocked side is now accessible has fixed the problem in my game many times. It's really weird.
Bathrooms are sometimes the worst for routing issues. The sim washing the toddler need to kneel next to the faucet end of the tub, so make sure that's not blocked by a sink or toilet or something.
If there are two caregivers for the toddler (for example, two parents) sometimes they both try to do something with the toddler at the same time and the game cancels the action for one or both of them. Make sure one of the adults is busy doing something else before having the other take care of the toddler.
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Edit to add one more idea.
Is there a stereo on the lot? Sims (toddlers included I think) will wake up and get out of bed if the stereo is playing, even if it is in another room. So that's one more thing to check.