If you have a lot of packing and several people traveling together, it may be easier to take the car. From Gothenburg follow the E20 to Vara, take road 187 to Lidköping. When you are in Lidköping, there is brown signs to Läckö Castle. From Stockholm take the E18 to Örebro, then E20 to Götene, take road 44 towards Lidköping and then follow the brown signs to Läckö Castle.
Läckö Castle on google maps>>