Most country around the world will recognize marriage oversea. US, Canada, EU, Japan, Singapore, HongKong, Australia will all recognize a legal marriage in any country. This is why lots of Israeli people get marry oversea as they don't have civil marriage in that country but will be legally married if done oversea.
So, if you get marry oversea and keep a residence in US, she can fly over to sue you for divorce and get support/assets. Don't know how that would works if you have multiple legal wife in Dubai. You can always marry a Saudi Arabia woman, since you will become her legal guardian and cannot leave the country without your approval (but she can always forge your signature or sue and have you replaced).
So, if you get marry oversea and keep a residence in US, she can fly over to sue you for divorce and get support/assets. Don't know how that would works if you have multiple legal wife in Dubai. You can always marry a Saudi Arabia woman, since you will become her legal guardian and cannot leave the country without your approval (but she can always forge your signature or sue and have you replaced).