WHAT DOES SEPARATION MEAN TO HER?
I would start trying to figure out the meaning of separation for her. This has two parts. The first has to do with her present situation. What are the emotional stresses that press on her soul right now? Are her parents and grandparents all well? (No illnesses or what she may take as threats of death?) And are they getting along reasonably well? (No separations or tensions that she may take as threats of separation?) Is she herself well? Any there any new siblings? Any parents of friends divorcing? Are any parents or grandparents of friends very ill? Anything in the news that may have frightened her personally? Any lost pets?
Sometimes you can identify something that an eight-year-old may need help putting in perspective, putting into words, or just putting up with.
The second part has to do with extra meanings which she may be bringing along from past separations or emotional strains and attributing to some seemingly minor current problem. (For example, she may have experienced a sudden separation from you because of family illness when she was four and shown no signs of distress at the time. But inwardly, she may have attributed your absence to her own feelings of anger toward you.)
This will be hard to find out directly from her, since she may be unaware of it. But you and your husband can try to ask yourselves if, in addition to her cautious temperament, there was a time when you may have noticed that something changed in your daughter; a time when she became less robust, seemed more cautious or low-keyed. You could try to imagine her concrete life at such a time.
MEANINGS FROM THE PAST
You may find you can pinpoint a time when she took an outside problem into her inner set of meanings and fixed it there. Sometimes this involves sibling births, her own or a sibling's illness, or loss of a security toy. Take your memories seriously and you may find something worth talking with her about. Such a talk would involve reminding her of the time, telling the story yourselves, playfully but respectfully suggesting the kinds of interpretations a younger child might have given, and how she might expand that interpretation now.
These two parts do not exclude one another. It is common to find an anxious child suffering from a combination of extra past baggage added onto a current situation.
There is a third point, which also coexists with the first two: her constitution. You could picture her as having a tendency with a threshold. When something inside or outside pushes her stress level over her threshold, she expresses her tendency to anxiety. This tendency is something that she may feel is bigger than her. You can help her recognize this tendency and have her be sure it is only a part of her, smaller than the whole of her personality. She may now feel that she lives in her (larger-than-herself) anxiety. We would want to help her to be confident that really her (smaller-than-herself) anxiety lives inside her.
You can also help her to notice what it is that pushes her over her threshold. If she is sensitive to separation, then understanding this sensitivity will help her put herself back under her threshold. And so will planning and anticipating what may make her anxious so she can gradually prepare for it.
She can alleviate some of the sensitivity by taking family photos, or an audio or videotape that she has made with you, to school. Often, having something like this available is even more important than using it. All this is in the interest of giving her more mastery over her fears.
If you find that you are stymied, you could turn for professional help. In that case, the results of your efforts will guide the professional to choose one or another of the three approaches for starters.
For you, it would be important to be confident that the problems you describe can be resolved, and your daughter deserves to become freer of fears and surer she's in the driver's seat of her emotions before she becomes an adolescent.