Sounds as if you lost the emulsion from the egg yolks - it should resemble Hollandaise but with more tang. Be sure to beat until frothy the yolks and lemon (sometimes water) and over a very slow flame heat until the yolks start to thicken. To that add the tarragon and shallots then begin to add the butter in clumps stirring after each addition.
Instead of fresh tarragon, you can also use tarragon vinegar with the lemon juice to start (since both are acids, use a combination of the two to equal the original amount in your recipe).
"Butter in clumps"......?
It's been awhile, but I've always used clarified butter when making a Hollandaise/Bernaise......add the tarragon/shallot reduction to the egg yolks ....depending on skill level you can use an open flame.....just heat gently so as not to scramble the eggs......a double boiler is more novice/user friendly.......slowly drizzle in the clarified butter while whipping the egg yolk mixture until you reach the proper consistancy.....loose mayo like........if the sauce starts to break , adding warm h2o can usually pull it together, serve immediately or hold for service in a bain marie/low simmering double boiler. It will be tangy.
I think perhaps I never had it emulsified. I went on a recipe from latrousse gastronomique, and here's what happened:
Red wine vinegar, 2 chopped shallots, taragon, reduced to about half in a pan. Strained and left to cool, then added 2 egg yolks and whisked in a bowl over a pan of hot water. Now the eggs didn't form into a thick sauce, despite me doing it for about 2-3 minutes. I think this takes more time.
Then I added cubes of butter, one at a time, which I'd frozen previously.
When I got through 125g of butter, it still wasn't thick, so I added another yolk and nearly twice as much butter, then some chopped tarragon at the end.
It was nice, like a tart mayonaise, and it didn't split or anything. So it tasted nice, but perhaps it wasn't bernaise.
it's kind of funny because it made enough for about 30 people and the rate we ate it (dipping the asparagus and chips).
I warned my g/f that it was basically half a stick of butter in each of our bowls!