Amanda, I'm pretty sure you won't have a problem coming into Israel with a British pasport, even if you have a visa for Dubai. You can even have a visa for Syria it doesn't matter (not sure about the other way around though).
If you could go through Saudi Arabia and then Jordan, I'm pretty sure you could get into Israel fairly easily and with the cats as well. Of course, you will need to make all the necessary arrangements before that. If this will ever be an option and you need any help sorting out Israeli beurocracy, just let me know.
If you could go through Saudi Arabia and then Jordan, I'm pretty sure you could get into Israel fairly easily and with the cats as well. Of course, you will need to make all the necessary arrangements before that. If this will ever be an option and you need any help sorting out Israeli beurocracy, just let me know.