I had a similar reaction at most of the significant partings we meet along the road to independence for our children: the first day at the child-carers, at nursery, and primary school, and probably one day I will cry at my son's wedding!
But we can't help how we feel, and I hope my friend won't choke her tears down if they come. They do come back to see you, some even move back in! And, although not all mother-child relationships are as good as they could be, it is a unique, immutable bond.
I first came across the following passage from Kahlil Gibran's wonderful classic The Prophet when I was at grammar school. As is always the case when something speaks directly to our condition, as Quakers say, I knew immediately that for me, it was a truth. I copied it out for my favourite teacher, and in the years since I've copied it out for quite a few others. I still love it.
Your children are not your children.
They are the sons and daughters of Life's longing for itself.
They come through you but not from you,
And though they are with you yet they belong not to you.
You may give them your love but not your thoughts,
For they have their own thoughts.
You may house their bodies but not their souls,
For their souls dwell in the house of tomorrow,
Which you cannot visit, not even in your dreams.
You may strive to be like them,
But seek not to make them like you.
For life goes not backward nor tarries with yesterday.
You are the bows from which your children
As living arrows are sent forth.
The archer sees the mark upon the path of the infinite,
And He bends you with His might
That His arrows may go swift and far.
Let your bending in the archer's hand be for gladness;
For even as He loves the arrow that flies,
So He loves also the bow that is stable.