Amman airport to Tel Aviv airport

Royal Jordanian Airlines show 2 daily non-stops.

It appears, from limited research, to be the only non-stop option.

You fly. It is a 20 minute flight.

From the border crossing, it's less than 1.5 hours drive to the Tel Aviv airport, but I don't know if you can get a taxi that can do that. It may be possible to arrange a private driver. AFAIK the only taxis that operate from there are based in East Jerusalem and don't have Israeli license plates so it would be a huge hassle to get into the airport in a West Bank car. If you have to go into Jerusalem and transfer, that would probably add at least another 1/2 hour to the trip, maybe more. I have no idea what the taxi would cost from the border. I think a taxi from Jerusalem could run around $80, possibly a lot more.

As Tom said, getting across the border at the north end of the Dead Sea, which is the shortest route from Amman to Jerusalem and on to the airport is often quite time consuming. That crossing, unlike the ones in the north and the south, is not generally used by tourists. It's meant mostly for Palestinian workers and people with special visas, like diplomats and such.

It sounds like you are planning to fly round-trip Tel Aviv, with a side visit to Jordan. Another possibility is to fly Turkish Air open-jaw from the US, into Tel Aviv and out of Jordan. I don't know the flight schedules for Amman, but Turkish has 4-5 flights (maybe more if tourism picks up) daily from Tel Aviv, so you can usually get a short (1.5-2 hour) layover in Istanbul. It's a very good airline and the transfer in Istanbul is very easy (I did it last summer on a trip to the US).