Once you are married at one place, you don't have to register your marriage again in another place. Whether you get a divorce in any place in the world, the effect is the same.
However, in terms of tax or any other social and family matter, it is usually recommended that you get divorce at the place where you jointly live the longest. You also may want to file where you most business and family assets or activities are.
The first person filed at a certain jurisdiction usually ends up having the pleading heard there.
So, you probably want to decide and file first as soon as possible.
California is a community state. It has one of the best protections among all the U.S. states for the lower earning spouse in general. I have not had exposure to Sweden's divorce law and tax.
It is suggested that you "pay" three top line divorce attorneys, three separate firms, just to consult on where you can and should file your divorce case to get the best benefit financially and for your children, etc. This is how important the matter is, which is worth you to look for a third opinion. -- three separate opinions.
If your wife sent us this request, I would have said the same thing.
Please feel free to follow up.
Fiona Chen, MPA, Ph.D., CPA, ABV, CFF, CITP