Small dog syndrome - help my little dog thinks she's the alpha?

We have a Jack Russel/Pug mix (Jug), and a Bernese Mountain Dog. The jug is 2 yrs old, Bernese is 6 - both female. I have read some about little dog syndrome, and am guilty of letting her on my lap (which I am going to try and control), and a few other bad habits. She is not snappy with us, nor food aggressive. it seems like she is trying to be alpha over the Bernese, which isn't working out. For example, today I was taking them out for a walk (not on leash - we have 46 acres, and we were walking in the back field). As soon as we got outside, the jug started jumping up, nipping and growling at the Bernese - which did NOT go over too well. The Bernese could kill her in an instant, although she is very gentle (there is about a 115 lb weight difference). I broke it up by grabbing the jug by the scruff of the neck. This does not happen often, usually because the big dog backs off, but today wasn't one of those days. Should I walk her on a leash instead? Inside, I have this same jumping/nipping problem when I go to let the Bernese outside, the little dog will do what she did today, and start jumping up nipping/growling at the Bernese. What is the right way to correct this?