Looking to go from Israel to Egypt to Jordan or vice versa

I think you're being completely irrealistic. With "two-three days in Egypt and one day in Jordan" there is no way you can see "Petra, Alexandria, Cairo, Luxor".... especially if you want to travel by bus.

It's a bit as if you were going to a birthright trip in New York City and told us you wanted to visit Mexico and its pyramids in one day.

Traveling from Jerusalem to Petra takes one day. Traveling from Jerusalem to Cairo takes one day as well.

It may look tiny on a map but in reality, the Middle-East is huge.

Error.

I think the same as catw. You might want to choose between the two destinations.

I agree with the above especially as you don't want to spend too much (and even if you could) your itinerary is unrealistic. One night in Petra is not enough to really see Petra and you need more time for Egypt. As you're on a birthright trip anyway why don't you say focus on Jordan and see all the religious sites there as well as Petra - eg Mount Nebo. You can relax more and actually enjoy yourself, it also won't break the bank. Remember the Pyramids have stood for thousands of years so I'm sure they'll be there in a few more when you have time and money to do a full Egypt trip.