The situation was certainly not desirable, but all things considered not out of the norm.
First of all, in comparison to other breeds, Huskies have a more feral temperament. This quality was highly valued by the Inuit who needed strong and independent dogs for their sleighs.
Then you need to keep the situation in mind: the rabbit triggered her hunting instinct, her adrenalin was running high, she had made prey and then you come around and want to steal it from her. Every but the most timid dog would have reacted that way.
What you did wrong was chasing her around. That only adds to the excitement of the situation and triggers her instinct to protect her prey. Instead, you should call her to you, take hold of the rabbit and hold onto it until she lets go. Do not pull it or yank it around, but make her understand that she should let go. That way you claim the rabbit for yourself instead of stealing it. Of course that is disappointing for her and she'll try to prevent you from taking hold of the rabbit, but it's better than pushing the adrenaling up even more.
My question is whether or not this might make her more aggressive towards us, or towards the other little dog in our household.
You don't have to be afraid of that. Wild dogs and wolves regularily kill prey to survive and learn to kill from a young age. The easiest prey would be their own pups or injured family members, but they know exactly who is part of the pack and who is suited to become the next meal. The only situations in which a dog would kill a pack member are severe starvation and illnesses like rabies.
Don't treat her any different or even seperate her from the smaller dog. All of you are one pack, keep it that way and there shouldn't be any problems.
You might want to avoid playing with toys that make squeaking noises when the dog bites into them. They simulate the death scream of a small prey.