What documents can I provide to prove my 3-year-old dependent's location for a visa application?

Nice try James

Not sure why you think submitting flight tickets from last year is a good idea. They want to know where you are today. Letter from the nursery doesn't prove anything. You need something that links you to the location that cannot be easily reproduced. You could take a photo off the applicant standing in front of a local landmark while holding a newspaper with today's date, or you stand and hold a bill in front of the house with the address shown both on the bill and the house with the date of the bill visible, or you buy something from a supermarket and stand in front of it with the receipt in your hand with the date and address of the supermarket visible in the photo. But you don't have to do just one of those. You could do all of them. And you can even also attach your rental agreement or whatever it is that links you to your accommodation. If you're not actually in the country of residence for example If you are applying in Southeast Asia, then you also can send your visa, stamp, permit, whatever it was that you got when you entered the country.

I don't think driving license is going to be a valid proof of location as you can take your driving license abroad.

What I did when I applied for another visa years ago in my home country was show a new document from the government proving my current registered home adress. They approved that document for both me and my daughter.

Are you in your home country or somewhere else? Which country?

Are you still in home country? Maybe a letter from their school or nursery if they attend with your address on it.