It is really important to teach your dog to walk appropriately on a leash NOW!!!
Trust me, it doesn't get easier if you don't make sure she understands walking manners now..
My big suggestion for that would be to scrap the harness, those things don't solve the problem they just make it easier to control the dog...
Use a gentle leader...Those things are absolutely amazing. Your kiddo could take her for a walk and hold the leash with ONE finger once she learned how to walk on it. The learning part is very brief. it is very simple and anyone can teach their dog to walk perfectly on it once they have really read and understood the directions..
Google Gentle Leader and check it out... Goodluck at the dog park. Maybe distance yourself from your DH and dog a bit at the park if you are going to be panicking the whole time.