Dachshunds

Hello,
I got a mini Dachshund ,born 6-11 and still having potty training issues. I didn't find out til later that this breed is nearly impossible to housebreak. I was working with two different sized cages, which I got for free. Then finally got the smallest cage I could possibly find 19 X 12.56 x 10. I though this fixed the problem , but I found a little present this morning when I went to take her outside. I have her a on schedule as best I can during the week, letting her out 3x a day at least, even at lunch time. But the weekends, I like to sleep in. Is that a problem, that the schedule is off?
When I first got her, her previous owner had her trained on puppy pads- which I don't want to waste $ on. I reward her verbally and with treats when she does go outside. I even have a bell on the door. But it's getting colder here, and the snow we get is deeper than the dog!
I've heard that some have trained their dogs to use a litter box?! Good idea or not? I already have a cat, and the dog is fascinated with it-sticking her nose in the box, or carrying the cat poo out of the box- another issue!!!!!Makes me crazy

I am at a lost, and pleading for help....... What am I doing wrong>? Please HELP.......