More about Browny,
Something you can try is laying down on the floor with your 5 year old. Let the dog come to you and when she gets to you then hold your daughters hand and show her how to pet her lightly but no where around the face or the tail. Just on the back or if she lays down on her tummy. I know how hard it is with a 5 year old because they get so excited when it comes to dogs. Well heck I still do and I'm 47!! LOL But the trick is going to be to make Browny feel as safe and comfortable around her as she is with you. If Browny sees that it's ok and you are laying by her, she may gradually also accept your daughter.
Another thing, let the dog take her time coming to your daughter and the step kids. I think the idea with the treat is a great idea. Especially if your daughter is willing to put a few like.... Honey Nut cheerio's in her pocket and give them to her one at a time. Of course warn the kids to keep their faces out of her reach, until you feel secure with her behavior. Let your daughter be the one that always gives the treats, if she is around, and if not you will give them or your husband. Dogs are not dumb, even the ones from the puppymills, if anything they are more shrewd than your typical pet dog because they have had to learn from a young age to scrap for every morsel of food and there probably was never enough to fill them up.
The crate I was talking about at Walmart costs about 16.00. Just a simple crate, but it would offer the dog and "escape route" when it didn't want to be bothered. She isn't going to stay in there forever, she will be too curious about whats going on even if she doesn't participate she will still be nosey and eventually want to see. The crate should be in the most out of the way place like maybe your bedroom, but farthest from the door to deter temptation for your daughter to keep going to look at her and see if she is still there. That would eventually cause another bad behavior since the dog would then possibly become territorial and it would only make a bad situation worse.
Fiinally, and the most important is praise. Catch more flies with honey than you do with vinegar.... remember that old saying. Time and patience, and a behaviorist or trainer. That should do it
One thing I do want you to know. If you can stick it out, and let her come around on her own, and remember she is really scared right now, you will find that ex puppymill dogs are the most loving of all because they are ACTUALLY grateful for the love and attention you give them. Nothing about you or your family will be taken for granted by her because she has come from such bad, that your goodness will literally make that dog want to lay her life down for you and your family. I will try and send you some links that you can read up on to help you understand where your dog is coming from right now, so that you can help her learn to be a good pet.