I don't know why the HOA just doesn't go get a flag for her an be done with it. The longer it festers the worse it gets and it's not that big a deal. Ask her to move the flag to a better spot if necessary. I'm sure someone can get a screwdriver to relocate it.
In NC the HOAs have major power including placing liens on houses for non-payment, etc. They have serious clout. I don't know how NH HOA laws are written.
I got on my board in NC because I hated how the grounds were kept and because our developer was not doing what he was required to do. I was elected president and then got the honor of having no life as it was like a second job with meetings, people coming to my house, calling my house, dealing with the HOA management company, budget, contractors, etc. It was a 400 single home subivision with common areas, some private steets, a pool, and I felt like a city manager
What I found was that most people don't understand what an HOA does and how it operates. If it truly bothers you about having restrictions on what you can and can not do with your home then don't go into an HOA. They can be both a blessing and a curse.
As far as covenants, I don't care what it is but when you take title of that property you do so with the understanding of what restrictions are attached too it. So to come in and complain after-the-fact will be met with my skepticism. Understanding the courts ruling, the law says American flags can be displayed so it's no use even waging that battle for an HOA.
Unfortunately from a legal standpoint many HOA restrictions are not very well-written to the point of being unenforceable. It you want to restrict something, spell it out in absolute language as if you leave ANY part subject to interpretation you're hosed if it gets challenged. Many covenants start with the developer sloppily getting them drafted or copied from a boiler plate before even one home gets built. The homeowners start moving in and most people comply to their intent and then you get "that guy" who will test the waters. In our HOA, fencing materials and styles was the hot item.
As for the landscaping, I got a landscaper to do it at at 75% of the cost of the national company and we got way better service and better plants.
Our developer got a huge fine from the City and had to rebuild the sedimentation ponds around the subdivision to current standards. Needless to say I was not his favorite person during board meetings.
When the annual meeting came up the next year I resigned and my wife made me promise never to get involved in an HOA board again
