I think you can still travel internationally given your dietary restrictions. When we travel with our two kids (ages 2, 4) food is always difficult, just because internationally its harder to find foods that they are familiar with and will eat. We eat healthy at home and as much as possible when traveling, but I'm not one to cancel a trip just because we'll need to eat out at a fast food place once or twice.
My suggestion would be to stay at American brand hotels that offer some sort of club lounge (i.e. Marriott, Ritz Carlton, Sheraton). These hotels, especially in Asia, often have a great variety of quality Western and local cuisine. These club level rooms can be had from free (via credit cards or status) to $200 a night for the Ritz Carlton club level upgrades.
If you want to be in complete control of what you're eating, then look into airbnb, vrbo, or timeshare properties, which are plentiful in most typical vacation destinations. I don't see any reason why you'd need to limit yourself to the US, I think you'd be fine in most of the western world finding foods that you are both familiar with and are healthy.