Wow Denise, great opportunity! I say without a single doubt...go for it! Because I know you can do it.

You might know I have shot two entire weddings now myself. Purely for fun/hobby without getting payed.(well I did get a very nice gift)Yes I'm still a big amateur so take my advice in good perspective.

What I have done with both weddings is that I have had a practice-shoot with both couples. I would highly suggest doing that.(for free?)
It gives you the chance to practice your skill, but it also gives you the chance to get to know these people and they get to know you. Which shows it's use when you're shooting at the wedding. You know how they behave and they know what to expect. I know you might do this without getting payed, but it's free practice for you as well. Also you could make up a good formula for example that if they like the practice shots they'd have to close the deal for the wedding day itself.
Doing a practice run also has another benefit. Social media is a big thing these days and if the couple is happy with the practice shots you get free advertising in the best possible group(age/interest) months/weeks before you shoot an actual wedding. A lot of time friends/relatives of the couple are in the same age-group(interests and behavior-wise) and it is very likely that the couple has connections with people that will be marrying too. Longer free advertisement = good for you.

As for equipment. I think your equipment(camera+lenses) would work just fine. Having a second camera(photographer) is a definite plus though. Learning your daughter how to take a few photos might workout better than you think. I'm still amazed how well my girlfriend takes pictures even if she doesn't have a clue what settings she's on or how the thing works.(yes, I'm working on that) And since I get the feeling your daughter watches your photography and the criticism you get, I think she knows quite a bit about things you should and shouldn't do already.

As for flashes and stuff. The bride has seen your photos and there isn't too much strobism going on on your site. Keep it that way. Unless you've got days and days to practice, just keep it simple at the wedding and don't start experimenting with lighting there. I took some product-shots today for a friend and the time I needed to set-up my flash/softbox(and I only have one) and all the other stuff simply would have been too long to do at a wedding. Better yet, some shots I still did with the flash on-camera. Which is actually not that bad if you bounce it. And a lot more simple. And also if you're doing a wedding there's more important things to worry about than flashes. Keep your stress-levels as low as possible.

If you're going to do a test-shoot. Ask your couple to google some photos that they like. Discuss the photos with them. Some might be possible and doable(perhaps you could test it after your conversation), but some might be out of your league. Discuss it so your couple knows what they can and cannot expect.
Also ask your family(son/daughters) if you could shoot their portraits to help you prepare for a wedding. They have experience and they can also guide you. Perhaps your neighbors are willing to help you as well. Consider it as an investment to your experience.

If it weren't for me being on the other side of the world I would have fought my fear of being in front of the camera and modeled for you. Perhaps someone else in your area at this forum will do it...

Good luck!