What is the shelf life of my home made coleslaw dressing?
Your coleslaw dressing is almost certain to be sufficiently acidic as to have an essentially unlimited (call it at least a month or two) in the refrigerator.   Commercial mayonnaise is acidic enough off the shelf to discourage bacterial growth pretty well, and you have enhanced its acidity with the cider vinegar.

The balsamic dressing--it is difficult to say.  It depends on how acidic it is, and that depends critically on the recipe.

See also:


Room temperature &quot;rest&quot; for fresh mayo?
Making &quot;long(er)-life&quot; homemade mayonnaise