Off hand, I would say that the vinegar and maybe not enough salt are the two main culprits. I would omit the vinegar from that recipe completely, and replace it with fresh lemon juice, but not at the ratio you have specified. For every dozen or so mussels, I would add the juice of maybe 1/2 a small lemon only. The recipe that you provided has too much acid, and of the wrong kind. Regarding the liquid, you're probably starting off with too much initially. You only need enough liquid for about 1/2" depth in the pan for steaming. Saute your aromatics first, then add the mussels and deglaze with 1/2 white wine and 1/2 clam broth (if you have it). If you don't have clam broth, then just use all white wine. Once the mussels are done, remove them from the pan. At this point, you can either swirl in butter off the heat (this will give you a version of the sauce used for pasta al vongole) or you can add heavy cream and reduce that until thickened. Make sure that you don't boil the cream and it doesn't burn. It should be at just a light simmer.
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