First, do speak to your neighbour. If she is a responsible cat owner, she will understand that this is a serious health issue and try to help you keep her cats out of your garden.
If I were your neigbour, I would suggest you flung a bucket of water over my cat, or sprayed it with a water pistol, until it or they took the hint. I would also feel obliged to put up a fence that the cats could not climb, but legally you cannot demand that she does so.
It is certainly harder to control cats than dogs, but it can be done.
Keep your greenhouse door closed and open roof vents to air it and keep it cool.
Open your house windows on a small latch, or install fly nets.
If a cat walks in, shoo it out. I realise that if it has shed fur you will still be troubled by the fact that it came in, but you need to make it clear to the beasties that you don't want them in your house.
Most cats dislike the smell of ordinary household vinegar, so in warm weather when you have doors and windows open, try placing a small bowl of vinegar on the sills.
Hissing like an angry cat usually deters them too. A recording of a dog barking, or a goose or gander hissing might work as a deterrent too.