We also used the bell. The last 4 dogs we had would ring the bell when they wanted to go out. But that was pretty much after the initial potty training was done. The bell works much better than the dog standing by the door until you happen to notice it. It didn’t take more than a few times of showing the dogs how to use the bell. When we would open the door to let them out we’d ring the bell ourselves and say, “ring the bell - lets go out”. Once in a while, a dog would be lazy and just stand by the door and I’d say, “are you going to ring the bell?” and then he would!
This actually sounds like too much fun. I may have to introduce it.
I’ve never had a small dog, so as far as I know their smaller bladders do indeed mean they need to go more often or with less warning. But I also remember housebreaking my (eventually ) very large dog - and there was a point where he wasn’t housebroken in the sense of only toileting outside and being able to wait for us to return/let him out but was housebroken in the sense of not peeing and poop wherever. By the time we had him for a month or so ( so maybe three months old?) , he knew what the the puppy pads on the tile floor were for. Which was way easier to clean up than secret stashes all over the house.
It may be too late for the OP, but what’s worked extremely well for us with puppies is when they first come home, watching them like a hawk, scooping them up at the first sign of impending pooping/peeing and taking them outside, praising outdoor elimination to reinforce good behavior. Never any puppy pads in our house.
Crating the stubborn pooper, keeping a close eye on her when allowed out and doing the scooping/outdoor/praising routine might eventually work. That said, our first dog (an otherwise intelligent cocker spaniel) was a sneak eliminator par excellence. Just a willful and stubborn animal.
Two words: dog door. I’ve owned several dogs in past years, old and young. Once they figure out how to use the door, never had an incident in the house, ever.