Most rational adults do not expect to be invited to every party, especially if they are not close to the host/hostess. Since this person has chosen not to spend a lot of time with the group, I doubt that she expects to be invited. Personally, if I was her, I would be very offended if I found out that a friend of mine was trying to bully a distant acquaintance into inviting me to party. I would wonder why my friend thought I was such a loser that I could not get invited to parties on my own.
As for the guest, I would refuse to discuss the guest list with him. If you give him any reasons for not inviting his friend, he will probably argue with you. He may even report back to his friend that you said something "mean" to her (even if you did not say anything remotely negative). Unless he is paying for your party, he does not deserve an explanation about your guest list.
I agree with Twik about removing him from future guest lists.