Hi, and welcome to the forum.

I'm a little confused about what it is you want to do with the online degree. It technically counts as a "university degree" if you're aiming for one of those visas that requires you to have one - but the H1 and H2 visas have very low caps these days, and once you find a job you may well find yourself subject to a lottery for the limited number of visas available. Whether your online degree will be accepted by potential employers is up to the employers themselves, though there is no shortage of hotel management majors in the US, and you'd need to have something to offer them in terms of "unique" experience to justify them going through the expense of petitioning on your behalf.

You may have to be content with the multiple entry visa (which is a great thing to have, BTW) and making periodic visits while your girlfriend is finishing school. Or maybe someone else will have some other ideas.
Cheers,
Bev