Be more patient. Spend time with her. Remember, it is heartwrenching to be a small child and know that "some other little girl gets to live with Daddy". Make her feel a part of your home. Be sure she has her own bed, her own space, her own posters on the wall, etc. Her own little dresser there. She is his child as much as the new baby and it is very hard on chldren to understand their own anxieties. Remember, she is NOT A VISITOR....she is your husband's child as much as little Ava and she is also the half sister of Ava. Give her "big sister" jobs to help you with. Praise her. Color WITH her. Make pictures for Daddy for the fridge. Take both girls to the park. Show her how to use an instamatic camera so she can take pictures of whatever she likes and then make it an event by taking it to the one hour photo shop and then make an album that is her special photo album. In other words, love her like your own.
DO NOT and I stress...DO NOT complain to your husband about how difficult she is. You will invariably create hostility later down the road in your marriage. (or sooner) Try to get rid of the "I deal with her" kind of thoughts. It will only make more negativity and create more problems for yourself...and you do not need your husband "to understand it isn't a vacation" when she comes? Why do you want him to feel frustrated and agitated? What are you hoping to accomplish? Do you want him to quit his job so he can be there for his daughter? I don't think so. What do you want him to do? Do you want him to cancel his daughters visits at his home? How terrible would that be for her, and him?
The best resolution for you is to treat her the same you do your own daughter regarding rules and benefits. Your husband will love you more when he see's that you care and love his little girl as much as you do your own.