D.K.
It may take some time. Have your friend give her daughter a sticker and kiss it, put it on her shirt and tell her that is for when she feels sad or misses her mommy.
Have her mom just kiss, hug and walk out the door, making it a least drawn out as possible.
Have a good distraction the second she leaves, a cool toy, movie, puzzle or snack, talk to her in a very upbeat voice, try not to coddle her if she starts getting upset but just get her involved in something right away.
It may take some time but the key to what you stated is she does find her way and calm down and ends up enjoying herself.
As for your son, remind him she just misses her mommy and it is his job to help her out not make it harder. Empower him with a task of helping the little girl feel welcome and find something for them both to do, playdough, anything to keep them busy.
Give it some time! :)