Litter box problems can be frustrating! Cats and kittens do not really need housetraining, in the way that dogs do and if they do not use their litterboxes, there is always a reason. We just have to figure out what it is!
First of all, do not feed her right next to her litter box. Cats are quite fastidious and do not like to eat where they eliminate if they have a choice.
You have a two story home and the kitten is loose during the day, correct? If you've had this kitten just a short time, I think she may well be in one part of the house when she has the "urge" and either cannot get to her litter box in time, or may not remember where it is.
She may also be afraid of the dogs, and choose to pee wherever she is, rather than pass them to get to her box. Four dogs, no matter how friendly, would be very intimidating to any cat of any age.
What I would do is keep this kitten confined to one room until she is using her box reliably. Also, if this kitten was a stray, I feel the automated litter box would be very frightening to her.
Try a plain litterbox (or two) for now with ordinary unscented clay litter in it ( you can switch to scoopable later.) You want to make it seem as much like the outdoors as possible. And of course, keep the boxes very clean!
By using these methods, I had whole litters of feral kittens and adult cats - who lived their whole lives outside - using the box unfailingly from day 1. Please don't give up on your kitty yet!
I hope this helps!