I think something doesn't make sense here. You are scheduled 10.5 hours per week. It seems like you are paying a huge amount for so little hours. When I read your copy of her letter it said adding one day per week would be $650 a week and $650 for full time.

What is it?

Methinks you approached the other client and asked them what they pay and what her schedule is with them. It doesn't make sense you lucked into that info with initiating it.

That is going to get you booted as soon as she replaces you so gear up for a termination.

If you want carte blanche to every day offer the full time rate and save the deal. If you want what you want and want it as a pay as you go deal you aren't going to get it. If you don't like being told no... you won't get a yes on your terms. You will be termed.

Bringing up the other persons arrangement will be vetted out with the other client. She has already done it.