Based on my experience, separation anxiety is triggered by being in an unknown territory. Your daughter might feel unsecure and wants to be within your security blanket. Best thing to do is talk to your daughter and tell her everything will be fine. Tell her you'll be outside if ever she will be needing anything. She may be peeping through the window a couple of times but sooner or later she'll get the hang of it :)
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Caring and Loving Mom of 3 :)