I'm sure you'll get lots of replies soon but it might help to have a bit more infomation
How long has he been with you? What history do you have for him? Do you know why he was rehomed? What support/advice did the rehoming centre/rescue place/people offer you?
> He has displayed a tiny bit of aggression when we try to show affection to our other dog,
It might be useful to know exactly what you were doing and what he did that makes you think he was being aggressive - was it directed at you or your other dog do you think?
> How do we make sure that our Lab becomes the dominant dog ?
Once he has settled in a bit, the two of them will probably sort this out for themselves. There is no need for your lab to be the dominant dog and in fact you can create problems if you intervene too much. If you elevate her position it may lead to stress and anxiety for both dogs. A swift pat, praise and a treat shouldn't be too much of a problem but if you are fussing her - he may have no idea what you are doing to her or what she is doing to you. It might look very peculiar to a dog that has no experience of this wierd human behaviour!
The advice you get may be different depending how long he's been with you. If it's only a few weeks or less then I would imagine you'll still be getting to know each other and he will still be adjusting to his new routines. This may be more of an issue for him because of his background so the more information you have the better able you are to understand his reactions. Your older dog knows she is loved and is likely to be very confident in your home so she isn't going to mind too much if you spend extra time with him. He will appreciate more 1:1 time and as he begins to trust you it will be easier to get the measure of him.
Some behaviours may simply be caused by lack of training or socialisation, have you enrolled in a training class? Check the
APDT site for more information and also have a look at the Kennel Club Good Citizens programme. You may need to walk him on his own for a while whilst you get him sorted - it's a lot easier to work with one dog at a time, particularly if he's strong. Also have a search on here for 'separation anxiety' there was a recent thread about a weim and some advice that may help you. I'll post a link if I can find it :)
Well done for rescuing this boy - is he a smooth haired vizsla?
Edited to say: Weim link
here, have a read of the posts by Teri and karenclynes on separation anxiety - hope it helps