Just finish the trade to get them out of your hair. It sounds like with you they may just have become impatient, have they been waiting long after 'doing' their half?

Since we don't allow proxy posts their behaviour towards other people isn't a factor in what would make a post from you valid, and this all sounds just like petty drama honestly (that's my opinion as a third party based on what you wrote, not a judgement as a moderator. That would require a more full account based on solely your problems with them including evidence to verify it.)