I've just had a look at your previous posts and can see that Mitzy has had these problems for some time and that you've posted about them before. Sorry to learn that the problems are still ongoing.
It's not easy to get the full picture on a forum and without knowing Mitzy, but my guess is that you have a few things going on with Mitzy that may not be related to each other.
Because she's smelling herself continually I would take her and a pee sample to the vet to see if she has a urinary tract infection. You could also ask the vet to check her skin and coat to see if he can identify what's making her so itchy.
I'd also try a change of diet. I know you already have her on a vet prescribed diet but to me it sounds like it isn't working. If you're sure she doesn't have fleas or mites then her diet is quite likely to be the reason for the continuous itchiness, and grains in the diet, especially wheat and maize (corn) are common causes of itchiness. Could you try her on a grain free kibble for a few weeks to see if that makes a difference? It can be difficult to identify some food intolerances or allergies (if that's the cause of the problem) but as wheat, maize and other grains are a well known cause I would be trying grain free for several weeks if she was mine, because that's easy to do and if it doesn't make any difference you've at least eliminated that as the cause.
Your description of her behaviour when you're out walking sounds like she's fearful. Laying down and backing off when people approach, and becoming distressed when she hears children playing are signs that she's unable to cope with those situations. The chewing sticks and digging that she does afterwards isn't excitement but is a stress reliever, a bit like you or I twiddling our hair or fingers if we're nervous in a situation. Wagging her tail doesn't mean she wants to meet the approaching people that she's nervous of but is most likely wagging in fear or appeasement. Tail wagging has all sorts of meanings.
Have you considered getting a behaviourist in to see if he/she can identify the triggers for Mitzy's fearfulness and come up with a plan to help? Having somebody come into your home to see Mitzy there and out on walks could identify things that we can only guess at on a forum. If you're on Facebook there's a group called Dog Training Advice & Support who should be able to help you find a qualified behaviourist local to you.
https://www.facebook.com/groups/374160792599484/It would also be worth having a browse on the My Itchy Dog website to get some ideas of possible causes of itchiness.
http://www.myitchydog.co.uk/