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You will have to have your foreign order filed in the California courts. Once the foreign judgment is filed with the California courts you will be entitled to enforce the terms of the order / judgment. US has commity with foreign countries and the enforcement of their orders. You should be able to have the same rights to enforce the Swiss order in California as you do in Switzerland. Hence I would claim all fees and expenses that you would be entitled to claim in Switzerland.
I Hope this information and suggestions are helpful and I wish you the best of luck enforcing your order.