This just shows me how a client can be too honest with a prospective therapist who exploits it.
I also think the whole thing, while completely well-meaning, is a bit too group involved and messed up from the get go. I think the adult niece should find her own therapist and work out arrangements with them without it being a family affair. If after choosing her own therapist and making her own arrangements, her mother wants to give her money - great. But I would not make the call/choices/decisions/hiring of a therapist for an adult for them.