There are many mothers that open carry on this site. It is not unusual or strange at all. I think that you will find that most people don't either notice that you are OCing or don't care. Don't worry too much about other people's perceptions, focus on protecting your family.
I think a mother with a gun is likely to draw even less attention than a man with a gun and a child (especially when your kid is yelling "let me go, I want my mommy as you're leaving the grocery store lol). I have been OCing for the entire time my 3-year has been alive and have never had a negative encounter. In my five years of OCing I have also never had any kind of encounter with the police so don't stress about that either. Just make sure you are aware of every law that relates to you as an open-carrier.
Now why wouldn't you carry to the grocery store or museum? My advice is to carry everywhere you are legally able to every time you leave your house. There is no such place as a safe zone.
Finally you should check out the Virginia Citizens Defense League. It is a great group dedicated to gun rights in VA. If you go to their website you can sign up for VA-ALERT (on the right side of the page) which is a free email system that will keep you informed about everything gun-related going on in the state. The website is http://www.vcdl.org