I find the whole 'lighten up' phrase offensive to the extreme. 99% of the time, it's used when person A has made person B uncomfortable, and instead of telling the offended person to lighten up, Person A really needs to apologize and make a note to self about sensitive subjects. We all have our sore points.
Let's put this in perspective:
Yes, she is a family friend and you like her a lot.
She has brought up embarrassing episodes from your life that you'd rather not discuss.
She not only told you to 'lighten up' when you expressed discomfort, but she intends to continue to tell these stories.
Your family enjoys teasing you, and given her status as friend, she could be part of a problem.
You are the bride/hostess, and you get to set the tone for you and DF's special day. I completely understand obligatory invites (kinda have that situation now) but IMHO, she needs to be left off of the guest list. If asked why, well, maybe being honest can make her an example that if you get teased and disrespected, you're simply not going to take it. (Obviously, I don't know you or the back story with your family, but this could be a great opportunity to set some boundaries.)
No one has the right to embarrass you or ruin your day. Just my two cents. I'd hate for you to look back on your wedding day with anything less than a genuine smile.