My advise would be not to use a blender. A blender can cause the part of the dressing in the bottom to get far to hot and this can retard emulsifying.
Dry mustard keeping things from emulsfying. Not hardley. I have been making my own mayonaise all my adult life and my mother before me and our recipe has dry mustard in it.
I have always had some trouble with dressings holding their thickness if there is no egg.
Is this a realy thick dressing like a mayonaise or is it just a sort of thickish vinegrette?
I would suggest using a hand held electric rotary mixer or one of those emersion blenders. Mix everything very well first, then begin adding the oil, no more than one teaspoon full at a time. If this doesn't work, do try adding egg.
When adding egg the perportions are, for one whole egg you will need 2 cups of oil. If you don't want to use 2 cups of oil, crach the egg, break it up with a fork and just use part of it. (incidentally all those mayonaise recipes that tell you to use 2 egg yolks: well, I have made mayonaise for decades using one whole egg)
And for those who are affraid of eating raw eggs, go to my website: www.thequestingfeast.20m.com
and go to the trivia page. You will find a link to a site that tells about egg safety. It seems that you have a chance of getting an egg infected with somonella once every 84 years. So go ahead, enjoy our Ceaser salad, mayonaise, egg nog and steak tatar!
And, good luck with your dressing.