Hola/ Marjaba!
I can help with Peru and Jordan- I lived in Amman for 4 years and moved to Lima in June. If you have 10-12 days on the ground, that would be a perfect amount of time for Jordan, and I think the minimum you'd want in Peru.
Weather-wise, March in Jordan will be inconsistent. Amman and the north (where you won't spend a ton of time) will probably be pretty good, but you could get rain and cooler weather. In the south, Wadi Musa (Petra town), Wadi Rum, and Aqaba (only if you have time) will be warm but not too hot yet. You'll want to watch the rain forecast for Petra, because it closes if there is rain, but you should be alright. I haven't lived in Peru in March yet, but I know that Lima will be quite warm and sunny.
Peru has a good system of internal flights, buses, and colectivos. In Jordan, you will either need to rent a car or rent a driver.
For food, Peru wins, hands-down. Jordanian food is very good but it does get a bit old after a while. Amman has lots of good restaurants. Peruvian food is simply world-class.
If you were to go to Jordan, I'd do this:
-Fly into Amman, spend a few days there. Explore downtown and do a full-day trip to Jerash. Also do a day trip up to Umm Qais if you have time.
-Two to three nights in Wadi Musa, with one long, full day in Petra. You could also Petra by Night.
-Two to three nights in Wadi Rum
-A night or two in Aqaba if you want some beach time or R&R, but I wouldn't prioritize this
-A night or two at the Dead Sea on the way to or from Petra/Wadi Rum
-There's TONS of other things to see in the country, with you have time, especially within about an hour's drive of Amman.
In Peru, you'd want a few nights in Lima (it's an amazing foodie destination, but there aren't too many big sights other than walking along the malecon), at least 4 days for the Sacred Valley (you could easily do more), and perhaps the Amazon if you have the time and the money.
$1500 would be tight for both destinations, but probably doable.