One of the most POWERFUL team building activities is getting them to learn to share openly and honestly.
Have everyone go around the circle and share:
Where they were born
Their birth order
The biggest obstacle or struggle that they have had to overcome
I would recommend that the doctor go first to be open an share with their teams. Once everyone knows each other better, lots of walls will be broken down and you can start to work together as a stronger, more collective unit.
I did what Anissa suggested today with my team. The team spirit has been down and there has been a lot of clicks, so I was surprised all the personal stories they shared. It definitely changed the negative tone that was there at the beginning.