A Cocker Spaniel should be automatically clean. I'd say you have either a puppy-mill puppy that had no opportunity to be clean, or you have a neurotic inbred one from show lines - probably an American Cocker (an extremely long-coated show breed) rather than a Cocker Spaniel (a medium-coated hunting breed).
What you have been "consistent at" is training him to NOT go toilet outside - you have let him play around then taken him back inside.
(1) You must remove all traces of his piddle-scent inside - there are products available from pet stores. Whether they will damage your carpet depends on your carpet.
(2) You must WATCH him, and as soon as he shows the pre-toilet restlessness you PICK HIM UP and take him outside. (You are going to have find your own solution to the "older dog outside" situation - naturally a puppy is going to want to play or scream (depending on its own nature) as soon as it sees another pooch.)
If you are a bit slow on the uptake and he's started before you get there you STAMP the floor and yell "NO!" as you scoop him up. (Yes, you CAN wash your hands after step 4, also the door-knobs....)
(3) You put him on the official toilet area and ignore him until he eventually decides to go toilet, and THEN you praise him and pat him, using over & over again whatever word you want him to associate with emptying bladder and/or bowel. (Northern hemisphere people discover that getting a puppy in November-December is NOT a good idea - it gets COLD outside, eh! But he's YOUR puppy, so you STAY there until he obliges.)
(4) Only then do you play with him then bring him back inside.
Once he knows that piddling inside is verboten, you either trash the special mat-whatever, or start placing it where he is supposed to go toilet outside. And naturally you praise him when he piddles or poos on it. ('Coz you're consistently praising+rewarding him for going toilet, not for using the mat, not for just being outside.)
Once it has HIS smell on it he is likely to use it, so you take it inside and watch him carefully and repeat steps 2-to-4 - he is still not allowed to go "inside", he is merely allowed to go "where his smell is". So the picking up & carrying is as important as it was with the previous training, and so is the foot-stamping; so is the YOU staying there until he obliges, at which time he is praised.
Training consists of rewarding desired actions EVERY time, and reprimanding undesired actions EVERY time. And timing is essential - praise & reprimand must be IMMEDIATE, not 5 seconds later.
And by the way, the older dog should have accepted the pup as soon as he/she sniffed your hand-scent all over the pup.
(1) A properly trained dog accepts whatever its human wants.
(2) Puppies are immune while they smell like puppies - especially while they smell like puppies with the boss's smell added - provided they have learned the proper submission postures to use when they've pressed their luck too far.
My youngest came to live inside at about 8 weeks old, when the rest of her litter went to their homes. She had the run of the house (until she decided to drag the toilet paper around, so the toilet door was shut at night until she outgrew that). She hardly ever broke the "Dad's bedroom is verboten" rule, she was happy copying whichever parent or relative was inside.
Les P, owner of GSD_Friendly: http://pets.groups.yahoo.com/group/GSD_Friendly
"In GSDs" as of 1967