Ugh i just typed out a whole page of advice and it all got deleted when I went to post it.... so here's the condensed version.
First and foremost anytime a behaviour that pops up that makes you consider rehoming your dog it is always advisable to seek professional help.
With this in mind I'd first like to point out that it could simply be herding behaviour. How old is your new addition. Herding breeds as a rule tend to be brutal for nipping during their younger years. When put under control it usually dies out but since she is a rescue it's possible that her ex owners never taught her what is and is not acceptable so even if she is older don't be surprised that she is still exhbitting a behaviour that is more common to puppies.
Duke, a Border Collie/ Rottie mix was absolutly terrible from around 3-6 months with this. Walks were considered prime assault time, any area within reach of his 4' leash were assaulted, legs,calfs,heels and shoes. Sitting on the couch, also prime time and if you wanted to get up to get something, oh my we used to sprint to avoid "jaws" as my brother nicknamed him.
We tried a few things that I read in my puppy books but one had no effect and the other simply increased his readiness to nip.
Yelping in a high pitched voice when he nipped only made it worse but because you mention she is pretty submissive she may respond well to this method so it's worth a try.
What really helped in the home was training a redirected incompatible behaviour. It sounds fancy but it's simple. Essentially Duke couldnt nip us if he was sitting, so in the house if he went to nip us we'd avoid the first nip and give a firm no and a second later command a sit, and the second he did we'd make a huge deal out of it, praise , toys, food the whole nine yards.
Most behaviours will simply die out when they are not rewarded but because in herding breeds this is an inherited instinctual behaviour it is important to teach her in what ways she can get out this need. The best way is to teach her to play fetch, as chasing the ball is the herd and then by getting her to bring it back she can continue to chase the ball.
However because noone on this board can see her body langauge and all of your family memebers during these incidents we are not getting the whole story, that's where a professional comes in. Also when you took in this dog you made a promise to take care of her. All dogs benefit from OB training and I would never say it's optional but in working, herding, and hunting breeds it's essential. These dogs thrive on learning and when left to their own devices often get themselfes in trouble because they are not given a proper outlet.
Kayla