I was saying try to get Jessie's birth certificate if she entered a delayed after her's got destroyed. If she had to write to IL to get the info on her mom, chances are she put it on her delayed bc (if she has one). Then at least you should know a good location to start.
I saw the note for Laura in 1900... luckily you can read it, because I gathered a friend was giving the info and didn't know about Laura's parents! There is a book out about the Foundling Hospital and it claims to include censuses. Have you seen it/had a lookup? There were some terribly heartbreaking letters they have on their website.
If the Mary J. Clark you have in Lake Co., IN in 1870 is the right one (living with Harriet and J.O.), she is listed in that census as being 31... I'm beginning to wonder if she really was older than anyone previously thought and maybe she is the mother of Laura Britton. That might also explain why the Clark folks don't want to talk about her with you. Maybe Mary told your Jessie something after Laura died, that's why Jessie knows Laura was from Kankakee, IL, but Laura didn't. I don't know. I'm guessing. I just don't understand how a girl who's supposed to be 20 is listed (clearly) at 31. Unless of course I picked the wrong Harriet, J.O. and Mary Clark in Lake Co., IN for 1870.