It's ok to wake a sleeping toddler
It's perfectly ok to wake a sleeping toddler. It's also best not be quiet around your toddler, either, when she is sleeping!
You can trust your small child's sleep regulators, her body clock and sleep pressure, to take the sleep she needs. If your toddler really needs to sleep, she'll stay asleep as you lift her up out of the stroller or car seat or cot, for the next activity you have planned.
If she wakes and cries, and she is breastfed, then you might offer a little feed to help dial her down. Or you might just think sensory motor nourishment. On with the day!
You can let sleep look after itself in the midst of a day that you enjoy, spent outside your home as much as possible, since our interior environments are so low in sensory interest for little children. This makes sure that your toddler's body clock is set in a way that keeps the Big Sleep for night-time.
Do you have other children in your care? Then you know how it is: school drop-off, soccer practice, play-dates, music class, kindy fundraisers - your toddler has to fit in with your busy life caring for his older siblings. And he does. He takes sleep during the day without you having to try, just whenever his sleep pressure is high enough. He takes sleep on the go, in the midst of the rich and changing sensory motor nourishment that comes with being by your side, as you and his siblings enjoy the outside world.