My first instinct was to try and see this situation from SD's perspective to try and understand her erratic behaviour in your home. I would guess that SD is feeling competitive, jealous and out of place when she comes to visit. When she's away from her Dad she misses him but in order to stay with him she is now faced with an army of other children on their home turf. With a maximum 2 visits a month I doubt she feels at home there, she must feel very much the odd one out and outnumbered by your children, and thus defensive about things which may seem minor to you or to them. It sounds like she arrives on the attack expecting to fight her corner and this sets the tone for her stay.

Now obviously there is no excusing for hitting and fighting, and it's possible she's just a mean girl, but if I were in her position I think I would also be experiencing a lot of negative feelings about the situation and you might do better addressing it if you can find out if there is an underlying cause. If I were DH I would take her on one side at a quiet time and probe a bit into her feelings when she is staying with you. I would set aside some one on one time with her to tackle possible feelings that she is competing for her Dad, and maybe review her sleeping/living/storage arrangements so see if there is anything that could be done to make her feel more settled. I would speak with your children to make sure they understand how SD might be feeling, and you and DH should be on the ball to intervene quickly in arguments before they get out of hand. Don't know if any of this helps but it's just some ideas based on the info you've given so far.

I would see if dh can set limits for her "this behavior isnt acceptable, if this occurs x will be the consequence." My so and I rarely fight when his kids arent here. They are with us eowe too. For a long time, and it still happens sometimes, we fight when they are here, because the kids are from different households and thus have very different expectations and consequences the majority of the time. So and I realized this and put a time out word in our vocabulary. Ours is purple. When things are out of hand in a discussion between the two of us one of us say it and we move to different room, change our tone and start making a plan. We dont discipline each others kids when a kid, cause we have five all together, is being nasty or something needs to change behaviorally, one of us will say the word and meet away from the kids to discuss what is happening and how we will address it. Its true that when one person.is in a bad mood and allowed to impact the whole group, everyone is miserable.