If it were me I would prefer every two weeks and here are the reasons .....as someone already stated she is concerned about I between weeks therefore I would be concerned too because she is telling you if the money is there it will be spent and she doesn't have the ability to put the money aside also if you didn't take a deposit to be used for the last two weeks of care she could walk and then you have nothing.
I keep a log of every payment ... When it was made, the amount, how it was paid (cash or EMT) , and the weeks that the payment covers and then at the end of the year I write one receipt per family.