She then insinuated that I was discriminating due to religion and performing an illegal act
This is bugging the crap out of me.
Y'know, just to shut her up on that front, I'd get right up in her face and demand to see the woman's licences to run a home-based day care, provide a DOZEN real references (not phony JW references), and insist on written receipts, and a viewing of every tax return declaring income from a home-based day care, plus have her audited by the Health and Safety Authority. If she can't or won't provide those, then say you can report her to the authorities for running an illegal operation.
Don't sow the wind unless you're prepared to reap the whirlwind. (Hosea 8:7)
And after that, it shouldn't be a problem for you because your wife will be mortified, and the JW lady won't want your child in her house.
Oh, and another comeback for this comment that you can give your wife is "You're a JW and I let you look after our daughter. If I didn't, that would be discrimination. I have the right to choose anyone, JW or otherwise to look after our daughter, and the decision will be based on what is in her best interests, not on whether the candidate has good Meeting Attendance™, or whether they light a menorah or go to mosque on Friday nights."
I daresay that since your OP indicated that the woman was interested in earning some extra money by providing child care services, there's a very high probability that this is a casual child care arrangement, without any legal registrations/licences/education etc. that would be required by the state. It sounds to me more like she wants to make "easy money" than take care of children.