You can do Petra in a day from Sharm - there are tours still being organised for that - but it is definitely not recommended as it is a very long day and you get only a couple of hours in Petra. It is also very expensive because the Jordanians have set their pricing strategy to penalise day trippers and try and get people to stay longer.
I would definitely recommend staying two nights there and one in Aqaba or three nights in Petra and also take in Wadi Rum.
Sharm itself is fairly busy with some hotels still closed. Not many Scandinavians at the moment and in the summer very few anyway but the packages holidays from Scandinavia will be back in full swing this coming winter.
However, if you are planning Cairo and Jordan, ( noticeably Petra and Wadi Rum ), then your tour will depend on your flights. I would suggest flying with Royal Jordanian, or Egyptair or Turkish Airlines, into one country and out from the other. ( I.e. Stockholm - Amman - Cairo and then Amman - Stockholm, or Stockholm - Cairo and then Amman - Cairo - Stockholm with Egyptair ). I do not know off hand which airlines operate to Stockholm but I am sure that Turkish do, so maybe you will have to do Stockholm - Istanbul - Cairo and then Amman - Istanbul - Stockholm. Very good airline and you can book through the multi destination option on their website.
If you do not want to include Sinai then you could fly between Cairo and Amman. But if you do want to explore a bit of Sinai then skip Sharm, ( or fly to Sharm ), and then head to Dahab, Nuweiba and St Catherine to explore that area and also to relax on the beaches and do diving and snorkeling there before heading over to Aqaba on the ferry from Nuweiba and then up to Petra.
This thread has more details on that area...
https://www.tripadvisor.com/ShowTopic-g297556-i10139-k11384534-Aqaba_to_Sharm_El_Sheikh_and_St_Catherine_s-South_Sinai_Red_Sea_and_Sinai.html#90498708