If you're local to Chessington (as I used to be) then TS very easy to 'just pop in' for the zoo/sea life/shows and not necessarily always bother with the rides. I used to lots, when my dds were little (4 and 2, older one disabled). But otherwise, yes, the zoo is not really the main part anymore, the rides/other experiences are. And yes, with 2 young children, it is so much easier with an extra pair of hands, just for getting on/off rides, sorting out the buggy/nappy changes etc. With or without disability.
I think this boils down to communication. It needs to be a LOT clearer, on both sides.
My nanny (have 3 dc, al have ASD) would not dream of doing anything like this to me. She would, however, be upfront about whether she could cope on a day out (we have Merlin passes too) and either I would go too, or she would only take 2 of the dc at a time, or she would maybe arrange to go with other nanny/carer friends and charges so that there were enough hands to go around. It would all be very clear beforehand though, as to costs and expectations.
It can be difficult to talk about money, but it needs to be done. If you cannot afford expensive extras, your nanny needs to know. If she cannot manage a day out, you need to know.
It sounds like it's time for a thorough talk about it all.