Yes, you must have 'joined' your spouse in Sweden, that is: come to stay, and preferably have stayed some weeks at least.
Your spouse needs to provide proof that s/he has 'sufficient means' to provide for self + spouse and other dependants. That is: either show work contract for job in Sweden or DK, proof of income, and copy of lease contract.
Your spouse must live or work in Sweden (or another EU/EEC-country or Switzerland) for you to be able to use the EU-rules. It means that a considerable part of the job must consist of services delivered in Sweden as well as frequent travels to Sweden. If you fulfil the requirements for family reunion according to DK-rules, you may apply for that as well.
BUT it will mean that you personally will have to fulfil a requirement of passing a test in Danish within 6 months, as well as other pretty strict requirements in order to ever obtain a permanent residence. A permanent residence is further a basic requirement for obtaining DK citizenship (there are may others, but before you reach that far, the rules will most likely have been changed several times).
Your spouse needs to read the info provided here:
http://www.aegteskabudengraenser.dk/raa ... et-EU-land
https://www.nyidanmark.dk/da-dk/Ophold/ ... retten.htm