Update: Jamie's mum is actively avoiding me
I've tried to talk to her when I saw her in the street (twice) and calling (once - the line was "bad" and she couldn't hear me).
Paranoid Stranger thinks it is because she knows its DD's party on Saturday, and she has no intention of giving me the opportunity to tell her face to face that she has to make sure Jamie doesn't insist on coming. Needless to say, I don't have any contact details for other family members either.
The way I see it, I have two choices.
I can ignore Jamie if (or when) she arrives or tell her to go home the minute she knock on the door.
I can prepare for Jamie to attend the party. DD did not invite her, but I'm sure she won't mind so much if Jamie is there.
If I choose option one, I can stop stressing about a gatecrasher, and address the issue of Jamie being dropped off without any arrangements being made at another time. Part of me feels that it would be the nicer (and easier) thing to do. I know Jamie will be very upset if she can't come to DD's party.