Completely understand, not doing the hob and sink properly is fairly standard stuff and the least you should expect. You're right to seek another cleaner in these circumstances.
I do cleaning and housekeeping too - laundry, watering plants, topping up pet water, bed making and bed changing etc. But I still won't do dishes. I explain this right at the start though, explain my reasons why and advise that I like to focus on the things that don't get done daily. Pots SHOULD be done daily when they've been finished with. Not left for hours/days/a whole week/a fortnight.
I do very detailed high standard stuff, so I don't want to be held up by dishes and have to compromise on my standards with the rest of the house because a mountain of greasy mouldy pots has slowed me down. Clients understand that when they hire me.
Because I do the rest of the house, the dishes are just one small task they have to do themselves. And 99% ofnthe time, they have dishwashers anyway. If they can't even be bothered to pop stuff in a dishwasher, then I'm lost for words.
Glad to.hear you have someone new though. Wishing you well. Hope they are what you need from a housekeeper. Just be careful.of how many pots you're leaving for this new cleaner. If you leave a lot, expect that some other area of the home will have to be left if they're unable to fit it all within a 2hr timeframe.
Clients having unreasonable expectations ie. a massive/varying list of jobs in an unrealistic timeframe, is a cleaners/housekeepers biggest reason for ditching a client (because cleaners dump clients as often as clients dump cleaners btw)