Policies vary so much on this. Partly due to provider's preference. In day care we do have to consider the hygiene issues that at home are less of an issue since there are fewer children.

That said - I require real underwear from Day one. I've just finished toilet training my 30+ child and in 2 weeks, age just 2, she is fully trained and hasn't had an accident here or at home since day 3 of training.

There are a few requirements I have before starting such as the child must be competent at undressing and dressing their lower half but I normally start the first business day after their 2nd birthday and that's proven to be fully effective for me. Only once did I have a child not fully trained in 2 week and we later discovered that grandparent who picked up from day care and kept child until parent finished work at 8pm, was putting her in a diaper as soon as she left here.

I do require diapers still for nap time and continue to use them strictly for nap time only until dry for 2 weeks. And I do require parent to start at home, the weekend before, and fully commit to my process. This helps them to understand what is required but shows me they are committed to doing it just as much as I am. Two days commitment from them and I'm happy to pick up the baton and see it through.

You decide on what works for you - your day home, your policy. That said, having these policies documented will always leave you in a stronger position. While I am open to client requests, I have also learned to be really clear that in my home, I have the ultimate say.

How old are these children you are referring to?
Are they able to dress and undress their lower body independently?
When they have an accident, other than cleaning up the child, do you leave them to find clean clothing and redress?