We have a problem with our dogs, please help?

As a dog owner I would say the collie is exhibiting dominant behavior rather than aggressive. This is a sad situation since the issues are obviously being caused by the old age of the jack Russell . I think putting the dog down is extreme. Also , as you stated, no aggression was shown towards you. It was an accident that you were bitten. Can you possibly separate them in the confines of the house? Put up a barrier? The older dog is probably content where ever he is so he could be put in a room and use a childs gate. He isn't going to be around for a very long time so it wouldn't be a long term adjustment. Wish you the best in solving this and I'm sure you will get some good advice.