I wouldn't say she's probably screwing another gringo. I would assume its a certainty. Is it really a problem though?
I guess it just depends on what you want out of a woman. I want companionship and support when I want it. If she's always there when I need or want her, then she's holding up her end. Within reason, who cares what she's doing when I don't. You can never control what another person does anyway when you aren't around. No matter what they say, it's best to assume anything can be happening.
50% of western spouses cheat. Cheating isn't uniquely Dominican. If kids aren't being neglected, house isn't being looted, money isn't missing, bills aren't left unpaid, and there isn't a disgracefully long line of guys waiting for you to leave, what difference does it make? Draw your lines in the sand and stick to them.
Maybe its just me, but I'm done getting upset because a woman lies to me or cheats on me. I almost expect it now.