Yes I think parents like that feeling and who can blame them ! I have the job to cuddle and play and they are rushing around trying to get lo fed , dressed and out the door ! I couldn't imagine my child being excited to play with another "mom" . In a perfect world I understand it is best for the child to feel connected to someone else but I'm not perfect and at times would prob feel badly as well !!
I would text her pics and reassure her as much as possible when you have the time , I may not always answer her texts so that she understands while you understand her feelings you have more than one child in your care and are not on call so to speak !!