Alright, I only read the first page, but I'm pretty sure I'm disagreeing with everyone here. My view is this:
The wedding is ABOUT the bride and groom, but not FOR the bride and groom.
The wedding is for the family and friends of the bride and groom, to have a public ceremony that allows the important people in your life to bear witness to the union, to allow them the chance to speak now, knowing that if they don't, they should forever hold their peace. To show before the world that the marriage is occuring, and to hold the couple out as married (A secret wife is, except in cases like Braveheart weddings, not a true wife IMO.) And also, in some cases, allowing everyone to meet the prospective spouse.
And last but certainly not least, I view a wedding as a party to say a retrospective and prospective "thank you" to all present for the support they've given you in the past and will inevitably give in the future. And that goes for everyone that you can think of inviting. Her dad's a total a$$hole? Don't invite him, but be aware that he HAS, at some point provided support to her. That doesn't mean it comes close to outweighing the negative, but so what?
My wedding was a lot of work (though not too much money because we were really careful), and I think that's the way it should be. My MARRIAGE is a lot of fun (and a lot of work.) But the wedding wasn't for us, it was for everyone else, and I wanted it to be good fun, and yet a serious matter, for all involved.
I also disagree with those who doubt your bride's sincerity about not having a big wedding. She very likely associates big weddings with being "all show and no substance," due to the failure of her first marriage. I know many people (particularly women) who had a failed first marriage and feel the same way.
My advice is to get all dressed up to mark the seriousness of the occasion, both to you and to your guests/witnesses, but have a very simple (but very public, be generous in who you invite) and inexpensive ceremony.
Make the reception lots of fun (and casual) - get a room (like an Elks' Club or something) and maybe a DJ (depending on your families tastes), and order some neat platters of a wide variety of food that people can snack on, but still fill up. Plan a "casual function" rather than a "wedding reception," and you'll find you can get a lot of the same things for 75% of the price or better. Seriously, I'm talking about several $10 veggie platters from your supermarket, cold cuts and cheese, some desserts.
You should be able to do it for less than the $3,000, and still make sure everyone has a great time. In my mind, at least, the two most important things are the public-ness and seriousness of the ceremony, and the fun for the guests at the reception.
Oh, and if people want to bicker, just say: "I'm getting married, and I truly want you to come. If you can't be civil, and aren't going to share my joy, please stay home anyway." People will get the point.
Best of luck.