we 'litter box" trained our chihuahuas but we dont use litter, we use pee pads in a box (as the male is a leg lifter)
it certainly sounds like this is a problem thats come from the breeder, puppies often house break much easier (no matter what method you use) if they can see their mother not going in the house or using certain areas ect...
it sounds like you bought from a byb who realy didnt want you to know that the dogs had no clue what the paper (or outside) was for, the fact you saw her mopping up after your pups parents too speaks volumes.
because of this id start from step 1.
you train to use a litter box the same way you train to potty outside, frequent repitition and praise.
firsly id suggest using wee wee pads in a wee wee pad holder or some other kind of box...a big plastic tote box with the front of the longest side cut out so she can go in and out. this gives the pad a much more visable physical boundry making things alot easier (its common for dogs to have front paws on and assume the back ones are on too...)
the nice thign with wee wee pads is they are treated with an attractant.
if you want to use papers i would still suggest using a box to form a boundry around the paper.
now, once an hour, imediatly after she wakes up, imediatly after a good play session and ANY time you see her displaying potty behaviours (excessive sniffing, circling ect) take her to that box, (do it more frequently if you have to...) tell her "go potty" and if she does, praise like crazy! if after a few minutes nothing, let her go about her buisness for baout 15 mins and try again...do this untill she does something and praise like crazy.
youll repeate this eventually stretching out the amount of time between taking her to her potty box...
untill shes going to it on her own.
dont move the box, make sure its in the same spot all the time so shes never confused.
part 2: make sure her bed is small enough, i do 100% endorse crate training, even more so if your trying to litter box train...the crate should be big enough for her to stand up, turn around and lay down comfortably, if shes pooping in her bed it means her bed is too big...(Or shes sooo used to sleeping in her own mess from the breeders that it doesnt bother her...if its the latter youll have a little more work ahead of you)
part3: when you cant supervise her 110% she needs to be in her crate or tethered to you...an unsupervised puppy is a problem puppy lol.
and i mean even if you jus tneed to go pee, make sure shes secured in a small area.
if you dont crate train you want to set her up a "safe room" a laundry room or bathroom works well for this...the smaller the room the better. she should have enough room for her bed and food/water dishes on one side of the room, and then on the other (but not more than 5 ft from the crate) shoudl be her potty box. when you cant supervise her 110% she shoudl be in this safe zone.
as i said, the rest is simply repitition, just keep taking her to her box and priasing...
dont give her chance to make a mistake.
if shes pooping somewhere she shouldnt be, its because you wernt being proactive enough or watching her closely enough...so just be much more active in taking her to that box.
now unfortunatly for you...while most puppies will naturally not sleep where they poop/ect...your puppy has gotten so accustomed to being surrounded by her own mess that its over rided that natural instinct.
so in your case your going to have to be even more proactive about it...make sure to never let her sleep in her pee box, make sure if she does have an accident you clean it up immediatly using an enzamatic cleaner, and never scold her for it...your job is now going to be 're-programming" her so those natural instincts of "dont potty where you sleep" can kick back in...so keep her eating and sleeping areas clean as possible and take her to her box frequently.
if shes having issues with pooping in the box you can put a little bit of poop on the pad, just a little schmear so she can smell thats what its for.
and again when she goes, be it with you putting her there or her going to the box on her own, make a big deal out of it
i would also suggest though, once shes getting the hang of pottying in the box you also train her to use outside as well...
because shell also be litter box trained shell never reliably tell you if she needs to go out, but by getting her used to pottying outside wil also mean if you go out anywhere your not tied down to taking pee pads everywhere with you ect.