I must have a very strange cat... she not only hates other cats, she also doesn't like me to be around too much! (As in she will ignore me, stay pointedly in another room and even start to 'grumble' if I'm at home all day for more than 2 days in a row. She does love to see me again after a short absence however.)
How long did your neighbour / pet sitter stay with your cat? I ask because I used to look after a cat for some friends. She was very nervous due to a difficult past, but also got lonely. So when I first started looking after her I used to go and spend a couple of hours with her (it helped that I was a student at the time and that Friends used to be on the television for several hours at at time of day

). She got used to having me around and then was less nervous, so that on later occasions I didn't have to spend so long with her, because she knew me and knew I'd come by regularly.
Just wondering if that might be a possible solution - get someone who can commit to longer than a 'hello cat, feed cat, clean litter tray, goodbye cat' visit during your April trips? I wonder if the fact that it wasn't the same person each day might have confused your cat?
I'm not an expert - my cat doesn't really care for any human company (I'm not even sure she's mad keen on me) and will hide from whoever pops in... but is happy as long as she gets fed. But the spending more time approach did work with this other cat.