Stephanie, I think you really hit on the answer when she told you she likes
you and is willing to pay you to be her friend.  She's really become dependant
on you.  She will gradually wean herself, but perhaps you could help this
progress at a more rapid rate by introducing her to other moms.  You might
want to bring a local LLL Leader with you to your next visit so this mom can
get to know her.  Or give her the names of other mothers with children close
to her children's ages for contact.  It might be worth it to offer to go to an
LLL meeting with her once.  She's paying you a high compliment.  She really
likes you.  I've had this happen in the past and these women, although truly
aggravating to me at the time, later became good friends.

As for the 3rd child throwing the mom for a loop I can attest to that.  Having
2 was no big deal for me.  But when number 3 came along it took me over a year
to get use to having 3.  I always felt that with two there's a hand for each
child to hold, and a parent per child.  It's not like that with 3.  It took me
three years to decide to add to our family.  When #4 came along he just
blended right in, no problem.  It sort of felt natural.

I wouldn't rule out PPD.  I think she really might have this.  Someone
experiencing it might not be in the best position to recognize it.  It's after
the depression lifts that moms realize how rough it was.

 Good luck Stephanie.  I know how very draining these clients can be.  Just
remember you're really doing her a service by providing her with the love she
needs.  Sue