I do not know where to start. You have no concept of how horses think or react and you give them a lot more credit for a lot more reasoning power than they have. Let me take it one thing at a time.
They began to bond to a very small degree.
Please forget everything you think or have heard about 'bonding'. They operate in the here and now and they work totally from a 'respect' aspect. No matter how often you feed them and brush them and say nice things to them, they are going to respond to each and every interaction you have with them according to what they have learned to do from your past similar interactions. In other words, you can feed and pet them until they die of old age and it will not make one bit more comfortable with you putting harness on them or driving them. They only respect you in the ways they have been given a reason by you to respect you.
I originally thought that they were so traumatized with the move from Michigan to here and they never got over it.
Again -- they operate in the here and now. They were never traumatized by their trip. Horses are sent or hauled all over the World and as soon as they are back on their feed and water, they are ready to go to work or train.
Now add the two wrecks to their traumatized little minds. And what have you got? A recipe for disaster.
Wrecks are unfortunate happenings that do shape a horse's future responses and reactions. All too ofter, they are reactions. The best thing you can do is quickly repeat the situation with controls in place that do not let another wreck happen. Sometimes you can just tie a horse up ad go through all of the steps that caused the wreck the first time. Some time you have to go so far as to use restraints that do not let the horse react and blow up and wreck again. I have driven horses with a front leg rope where I could pull up a front leg when the horse tried to bolt. I have harnessed horses with 4-way hobbles on them so they had to stand still and find out there was nothing to fear and nowhere to go. One thing is sure, the sooner you do it and get the horse past it, the better the resolution is.
so I will just work with them and see if we can't get over their lack of trust
Put all of the 'trust crap' in the same deep hole you put the 'bonding' crap. I know it sounds a little crude, so I will apologize in advance, but I just do not know what else to call it. Horses 'trust' those that they respect and know (not think) have the leadership qualities that they SHOULD trust. Look at it this way -- Why should they trust you with their lives and well-being when they do not even respect you enough do what you ask them to do? They won't. They have to look up to you as a leader and as the 'person in charge'.
Although the trainer had absolutely no problems with them.
This tells me that I am right. It is not the team as much as they do not respect you. You have put pressure on them and have backed off at the wrong time. You have taught them that they are in charge and it is a very big, new scary world for them and need a leader that does not accept any foolishness from them.
Everything they do is exactly what I would expect them to do. Given your age, I think you bought the wrong team. You should have bought the 20 year old team the breeder used to train the young teams.
These horses need a job, not more training. Do you live in ranch country? They need a job on a bobsled or a feed wagon and need to feed someone's herd of cows all winter and then need to go to the draft horse sale. If you still want to drive a team, find an old semi-retired team that will take care of you.
I am 65 and used to break feed teams for ranches in the Western Colorado mountains where ranchers still fed with teams in the winter and quite a few still put up hay with teams. I have a LOT of experience with training teams and quite a few of them came after big-time run-aways or other wrecks. I would not take on driving a young team today with all of that experience behind me.
I hate to sound so dismal and wish I could be more encouraging, but I just cannot think of a good resolution for you and a young, half spoiled team. I have had Hafflingers in the past. They are more 'quick-footed' and more reactive than the heavier breeds. I had no problems with them. There are a lot more of them around now that there was back when I broke a lot of teams. They are sure cute. There are a lot of them around here now. I do not know of anyone that has any problems with them. The local parades always have several teams in them. Billy Cook [owner of Billy Cook Saddle and Harness Co located here in Sulphur, OK] has a nice team of them that pulls his wagon in every parade. The Amish East of us have a lot of Hafflinger teams and I do not think they have any trouble with them -- but then they sure do not take any foolishness from any horse.