Hello to everyone and their 4-legged kids!
THank you all for the time you took to read my questions and reply. I am most grateful for all the advice. I have tried to follow the great ideas as much as possible and can post an update if anyone is interested.
Lyla (whose photo should appear with my posts as I've added it at least twice; no idea why it doesn't?)
is now more than 4 months old. Still a puppy but by miniature dog standards, closer to an adolescent.
I've read a lot about Dachshund temperament and they are definitely hard to toilet train and to train in general. Not motivated by pleasing their owners much! Not stupid, but just not willing to do what you want them to at the time you want - only if it suits them.
When she feels like it, she will sit, stay, stop, come, walkies, etc. I.e. she knows what you are asking, but just does it on her terms.
She is still not toilet trained and still has the occasional accident in her bedding, despite having other more suitable places to go easily accessible at the time. She, unfortunately, does not show much of a disinclination to soil her bedding!
At least she is more mature and doesn't need to eliminate as often as when younger.
We make mistakes also! You'd think with 5 people in the house, she'd get enough supervision, but that just doesn't happen with our super-busy lives and responsibilities.
She may pee on anything lying around; plastic bag, paper, floor towel, sports bags (2-legged kids need to learn to clean up after themselves better!), etc. Will never go in rain, even if full bladder; she manages to do a mini-pee and do the rest indoors after the walk!!
For a while, she'd make the effort to go on her puppy pad/newspapers laid out, but we have regressed a bit since then and I've no idea why. We are having a doggy door installed so when that's complete, will get rid of puppy pads, but at the moment it is either keep her outside and listen to her cry or keep her with us and provide a puppy pad/newspaper (always in same spot).
Pooing is just random anywhere, unfortunately.
She is still so excited by going out that it is extremely rare for her to pee or poo on any walk or run (yes, she runs faster than me!). Tiny legs, crazy, energetic, lively dog! Sharp teeth, too! Bite, bite, bite, run, run, run, jump, jump, bite, bite, bite...
We are working on it, however. After a 2 hour walk and no peeing for 4 hours prior to that, it had to come eventually and we are starting to really reward with absolute favourite snack whenever toilet happens outdoors.
Maybe we just didn't party hard enough? Now, no-one goes out without a special treat in their pocket.
Indoors, we just didn't pay enough attention as it had to be absolutely constantly. The second you weren't watching, she'd be doing it!
Now we keep her in her enclosure with bed and pad when we can't watch her indoors, otherwise we just let her whine outside if we are simply too busy, but obviously this is not ideal. Ideally, we'd be outside too, watching her ready to praise her.
Have tried expensive enzyme spray and washing bedding very hot but perhaps we don't use enzyme spray enough as it's so expensive! Will try the one brand you mentioned, Harry's mum. Have just bought several new bed pads so can throw old ones out (they're only $6 each). BTW, congrats on training Teddy! Big achievement alone. Loved your heart-felt advice from the 'trenches' as it were.
Have even tried those biological pheromone drops that are supposed to smell so good that dogs have to go there; she just wants to chew whatever the drops land on! More expensive, failed experiments!
OK, I'm in it for the long haul and will look forward to the first year being better toward the end of it!
Choo choo is so delightful in so many other ways, we just have to work on that association that going outside is good, and going inside is NOT good!
Now just have to tame all that biting, also!

Thank you all again for your help.