puppy misses step kids when they are gone

I can't believe I didn't think about this when we got a dog. My daughter is 7 and we have her all the time except for every other weekend. This summer we have my two stepsons also about every third week and every other weekend. After about the second week with the boys she fell in love. When they are gone she literally sits on the couch and whimpers, clings to us, follows us everywhere, looks sad and it seems like no matter how much we play, pet, do tricks, take her on walks, nothing helps.
We finally got out a dirty T-shirt of my stepson's for her to smell and that helped a little bit but she still looked and acted sad.
Now that school is starting we are only going to have them every other weekend. Any ideas for how to help her adjust? She is a rescue, 8 months old, and has a history of being returned to the shelter twice by families.
I know she has attachment problems and who wouldn't? I just feel so bad for her because how do I tell her they are coming back and it's ok?