Ok I'm sure I'm missing something here but ... why would you CARE about upsetting her by asking her if she's unhappy with your relationship but NOT care whether she dates other guys???..
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If ur gf's dating other guys ... that should pretty much tell you she's NOT happy in the one she's in with you...
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Maybe you should raise the bar a little friend, try and go out with girls that ARE HAPPY to be going out with YOU ... which will inevitable make YOU happier...And as a result of your happiness, they'll be happy ... and so on and so on .....
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Angie..
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I'm the yin to Carlos' yang .....

If a girlfriend falls in the forest, and there are no guys around to hear her, does she make a sound?..
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I can't seem to puzzle out what the question is, here, but nonetheless I would advocate for two things in any relationship: ..
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1. Communication and at least a modicum of honesty. If someone isn't happy, they need to address their issues with the other partner. Same goes for a person who suspects their mate isn't satisfied; this needs to be addressed...
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2. Fidelity. An "open" relationship can only be possible if both partners are happy with one another and agree on the circumstances of, er, openness. If one person is sleeping around because they're not happy in the relationship, then it's not an open relationship -- it's cheating, and it is (or should be) the beginning of the end...

What?..
It's okay to have a state-of-the-union talk and ask your girlfriend if she's happy being with you -- or if she'd like to see other people and explore her options. ..
I don't like that you're trying to track her moves. I think you should be upfront. Tell her she can see other people if she wants to...