I totally sympathize. And, while some do manage to work around it with "repackaging," or by dating others outside their triad, it can be difficult (for one thing, while love is not an infinite resource, time is). The reality is that, in a triad, if two of the partners are married, there are some practical issues that are difficult (and, depending where you live, almost impossible) to get around because of our societal model of marriage. It can leave the "third" in a fairly vulnerable position, even with everyone having the best intentions.
That isn't to say it can't work, of course. Just that there is a lot to consider, and you are not wrong for feeling like social conventions can make a difference. There are a lot of built-in protections in marriage (at least here in the US and in most European countries) that are a large part of why many people get married, that aren't generally available to a third party in a relationship (and, depending on the state in the US, very little can be done about some of that, even with a slew of contracts, etc., if two of the three are married).
It's worth weighing, for practical and emotional and time reasons, what is right for you, given your long-term desires. You could decide to date others in hopes of finding a marriageable partner, you could decide to request that you be one of the two partners in the marriage (if you're in the right place, you could marry her, even), you could decide you are okay with the idea that you will not have the societal protections but the other two will, you could discuss with them the idea that none of you marry and instead look at other options for financial and practical issues.
There are no right answers, except what is right for you, and for them, and for your relationship. But, you are not wrong at all for considering what societal norms may mean, or feeling potentially vulnerable and hurt at the idea of not having them.