We make about a pint of "base" dressing (6:1 extra virgin : w. wine, tarragon and garlic vinegar, salt and black pepper) and keep it in a stoppered bottle. Shake it up, pour required amount into a small dish/jug and whisk in any desired extras to vary the taste, although the flavoured vinegar means it's fine on its own. A pint will last us about a week and we don't notice any staleness.
Whisk it in. The mustard will actually help the emulsion - at least that's been my experience whenever I forgot it!
Salad-dressing emulsions are a lot more easygoing than newbies tend to think they are; though they will separate if left standing for long periods of time, they come back together very easily.