The only way to ease their reliance on each other is to shift it onto you.
The dog that has trouble working away from the other will automatically be thought of as the lower member of the pack....beware! This may not be the case. It may the alpha of the pair and unwilling to let it's responsibility go ungaurded.

So your first job is to work out which of the two is the dominant. Which one goes through doors first, which one sits back at feeding and at times when there is only one person to give affection? This may not be as obvious at it seems as the dogs have had some time to be comfortable in their roles and have it all well sorted out. You may have to watch them very closely to fathom it out. (If you need more help with this email me and I will reply......eventually!) It is not always the obvious one!

Your next step is to reinforce that the alpha dog is the alpha in the pair and be trustworthy in petting him, feeding him, taking him for training and putting on his lead first every time.

Your next and parallel job is to make it clear that the responsibility for the entire pack now lies with you and not with the alpha dog.
So, although the more dominant of the two dogs gets everything first, you decide and CONTROL when and under what circumstances anything is given.

This can be hard, especially with such new dogs that you really just want to hug and love.
You have to think like a dog and behave like an untouchable leader in their eyes. They have to trust that you are better than them at everything attatched to their security, well being, food supply, defence of territory and when it is 100% safe to relax and have no worries at all because you are taking care of it and it is not their concern.

To do this you have to be able to speak dog.

Both dogs get totally ignored at all times - you walk through them, not around them. You don't look at them. You don't talk to them. You totally pretend they are not there. As soon as both dogs are relaxed - that means lying down and not watching you constantly- for five minutes you call them both, give the sit command. If they comply you praise the more dominant dog first, give a treat if you like BUT make it a very small taste of something! (They have not done anything very special - just come and sit. If you start off with huge rewards then the reward will seem too small for later actions you request.) Then ignore again until they have been settled for six or seven minutes.

Carry this on all the time you are with them but vary the amount of time they must be settled before you call them. 5 minutes upto two or three hours eventually. (Dogs can tell the time up to a point - if they are called every five minutes and rewarded it will not take long before they are up in your face just at the five minute point and then shortly before - this defeats the purpose so avoid it!)

If you are leaving the house make sure there is a significant time period between your last interaction with the dogs and when you actually leave - so if you know the dogs will take about ten minutes to settle, let them out for a toilet at least half an hour before you leave.

If you are entering the house the same applies - you give them nothing, not even eye contact, until they are settled and leaving you well alone. Many people find this the hardest as they mistakenly interpret the dog's greeting as a sign of affection.
It isn't.
It is a highly ritualised behaviour to retain pack bonding and status. It makes the pack feel safe and trust their leader ever more deeply...as long as that leader responds in the proper manner. The leader MUST ignore all those that it feels are less able to lead the pack than it is. Any recognition gives the signal that the leader is unsure who the Alpha of the pack should be.

Do this for a couple of weeks, without seperate training for the dogs. Then gradually phase in the training sessions you wish to have - it really won't be a problem.
Your dogs will both look to you as the leader, training will be easier with each individual and their bond will remain intact.

You sound as if you have found a good trainer too, have great dogs and are surely destined for success!!

Let us know how it goes, good luck. Any questions, please feel free - but don't hold your breath while waiting for an answer at the moment!!!!!