Littermates

In general the trainer is right.  BUT, that doesn't mean you have to rehome one of the pups.  You're doing the right things by walking them separately and toileting them apart.  This is the kind of thing you need to continue, even going as far as separate play and training times for the pups.
 
This is my experience once pups get past the weaning stage....we foster and I always seem to have a litter......I always seem to be the most key critter in their lives.  They vie for my time and attention and are far more bonded to me than to each other.  Sure, they still like to snuggle up together, but they'd far rather be with MOM.  I don't think that I'm all that special....but they still prefer me to one another.  One of my fosters came back and immediately claimed me....he'll fuss with his full brother for the prime spot closest to me.  And even with the seven I had in the last litter, even tho they ALL went out together for potty time, they all got leash training one on one and all got their little mini training sessions one on one with ME throughout the day.
 
I now have six german shepherds (I'm not very good at fostering..I've failed 3 times! [&o]) and they all prefer ME to one another, so it CAN work.
 
All that said I wouldn't send two littermates home with a new owner unless I was DARNED sure that they were savy enough to really understand what they need to do to insure that the pups bond to them.  But it sounds like you have a good jump on things.
 
I think you're new here, so welcome to idog!

Hi,
  I have 2 Puggle pups, 1 male, Bubby Boy, 1 female, Baby Girl, 1 week apart in age. Not from the same littler and they are always together, they can't be apart, except Baby takes longer to do stuff outside and Buddy all done and wants to play so we bring him in. But they love and adore us as much as they do each other?
I couldn't and wouldn't keep them apart? Hope this helps.
                                                                                     Mary & Babies

No offense Muddy, but you are doing this the wrong way.  They CAN'T be apart??  What happens if one is sick or injured and needs to be hospitalized?  What happens if one dies?  This is NOT a good situation and is exactly what the trainer was talking about.  The pups are bonded more closely to one another than to you.  YOU need to be the center of their universe, not each other.

Lining up behind Glenda on this.  Dogs that have another dog as their center never develop to be as reliable and easy to live with as dogs that recognize the person as the primary individual in the universe.  In Muddy's case she may get away with this a bit, but in large dogs, especially those in the working and herding groups, that can make for some pretty difficult management.  A dog that gets its support from another dog is less likely to follow commands that will keep it safe  (leave it, come, stay) under distractions.  Glenda also brought up, what about when they must be seperated (it could happen, sooner than you think).  Why have them feel abandoned.

Training exercises that leave dogs in crates in different rooms.  Training while one is crated and one is not when they can see each other.  Taking one for a ride and leaving the other home.  These types of activities can help.   You do however need to be really vigiliant for signs of over bonding and act accordingly.

Ditto to what's been said so far.  Littermates should not be adopted together, unless there are unusual circumstances.  They will bond more closely with the littermate than they will with their humans.  I can only imagine the circumstances that could occur where one they are seperated out of need and both mope around and pine for the other.  It's ok to have more than two dogs, but they should have a difference in ages and should be allowed to do seperate things and have quality one on one time with the alpha, in this case that's YOU the human.