Hi there,
I don’t have personal experience with bonding groups, but I know the space is very important. With 4 bunnies it should be very large (probably 3 or 4 x-pens linked up). With groups, what can happen is a fight starts, one bunnies tries to flee, then the other bunny thinks that bunny is starting a fight, and then the aggression spreads around. You want the space to be big enough, and with enough obstacles, that the bunnies can interact and retreat when threatened without that causing more fights.
It also needs to be really neutral. Since the bunnies are mostly free-roam, your whole house prob smells like bunnies, so it might be hard to find neutral space.
Some people will also focus on the more difficult pairings, but since group dynamics are different, others recommend working with the whole group.
You also mentioned that they are all OK for a bit after the car ride at the beginning of the session. Try ending the session before things get testy, even if that means the session is very short.
You can also use the technique of petting the bunnies a lot and swapping scents when they approach each other as a way to stop fights, especially the two that are aggressive towards each other. You must prevent fights before they start or the rabbits will start building a grudge towards each other.
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The answers provided in this discussion are for general guideline purposes only. The information is not intended to diagnose or treat your pet. Seek the advice of your veterinarian or a qualified behaviorist.