Potty training her might the solution, if you hav ethe time to do it and the enrgy to wipe the floor... You might be suprised at how quickly she understand the whole thing, having an elder sibling also makes it easier.
My youngest is about the same age and doing the same. I used to put her down for her afternoon nap without trousers, but now I can't as she just removes the nappy. I have to be very fast to put a nappy on her as she doesn't want me to. She had a very bad rash few months ago and wearing nappies was very uncomfortable for her, since then it is a real fight to put the nappy on.
Every evenin I leave her without a nappy, she is going on the potty by herself, but miss it quite often though. I am the one delaying it, love the nappies too much