Need advice on how to handle a mother of a child in my daycare please!

[mom-in-alberta]

I would absolutely tell mom that even though her intentions are good, what she is doing is only making it worse. Chances are the anxiety is coming mostly from mommy, and the child is just sensing/feeling this.
Let her know that for everyone's sanity, you need her to arrive at the anticipated time (no earlier!), drop and go. Get her to use the same script daily, so little one knows what to expect. ie; "Mommy loves you, *kiss*, see you at x-o'clock!" (Happy, positive voice is super important here!!)
I would NOT be inviting them over on weekends, as it will only be confusing to the child. She will not understand why sometimes mommy can stay, and sometimes mommmy cannot. Not to mention, you put in your time. Early mornings, extra time on the weekends.... no way!!
As the others said, give this method a couple of weeks to see some improvement. If there is none whatsoever, then I would be telling mom that she has not adjusted and perhaps a different environment would be better suited to them.