Hi Seaway, :-)
Firstly I don't think that anyone has been rude at all, you yourself are stating the conditions that the pup was bought in, which is going to put forward the question of why buy if it was so unsanitary.

We always try our best on this site to help those who are not in the know, to not make the same mistakes as many before have and buy from not the best of breeders, so it is a valid point to make, no matter how far one travels. :-) Puppy farmers exist because people feel sorry for the pups so buy them anyway, when they really should just run. ;-)
Anyhow, I hope that has cleared up your worries, we just try to point out that the pups conditions were wrong. You have your lovely pup now.
As an occassional breeder my pups are trained from 5-6 weeks to follow me outside to toilet train and many, many good breeders also do the same so that when our pups new owners collect them most of the hard work has already been done. ;-)
Unfortunately, when a pup is left to sit in it's own urine and solids and hardly cleaned your going to get a pup that will naturally not know what to do, making it so much harder for yourself, as I am sure you have found.
You see the plus side in having a fully trained dog 18months - 2 years and then introducing a pup, is the dog will also help train the pup and when it comes to toilet training the pup will follow the mature dog outside and learn much quicker.
Finally the solution. :-D
Just continue with praise and reward everytime your pup/pups go to the toilet outside. Ignore the indoor toileting and make sure that you use a bicarbonate of soda cleaner this is the only thing that will get rid of the smell, bleach and disinfectants do not cover the scent of urine, although we can not smell them, pups and dogs still can, so will continue to pee over and over again.
Your older pup is marking over the youngers scent, just keep vigilant follow both around and even if you have to pick them up midway do so and let them finish outside with a big load of praise even if they just do a dribble.
It is very hard with two pups together, many here speak from experience of that. Good luck, just keep on top of them both it is the only way to train.