While I agree with others that it's not your problem she can't pay her bills, I personally would have no problem trying to work with the parent to come up with a solution. Maybe she could switch to paying weekly if 2 weeks at a time is hard for her to budget? As long as it's always in advance you would still be receiving the same amounts. Never provide care without pre payment!!
I understand your feelings of wanting to be charitable can make dealing with these situations difficult for you. You have to come up with a plan that you feel comfortable with. As she is a fairly new client you are right to be wary of this becoming an ongoing problem. If you do decide to allow her to pay late, make sure to stand firm and never let it happen again.