The E-2 is applied for at the consulate usually, so she would apply for it in her native country and it usually takes the same time as getting a non-immigrant visa appointment. It doesn't really matter where you get married. The E-2 does not lead to GC unless you are just an employee or you own only up to 5% of the shares of the company. To get an E-2 you must be an investor and own at least 50% among many other requirements but if you do than you cannot have the company sponsor you. She can apply for a separate work permit once she gets her E-2 as your dependent here in the US.
I agree with my colleague and would add that it doesn't matter that she's from DR and you're Swiss: she will be applying as your wife. She will still need to apply at the US consulate in DR. How long it takes depends on a number of factors.
See the informative article below: "The E-2 visa is a nonimmigrant visa, meaning it is temporary, while green cards are permanent. Moreover, a green card through investment requires a dollar investment of $1 million or more, while an E-2 visa has no dollar minimum."
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Estimated processing times are as posted on the Department of State website.
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