Really, gone are the days when people followed exact etiquette, so many things are different nowadays. If when they eloped, they did not use a reverend/pastor/priest, they may feel that it's important to have that done. It's really up to the family on both sides how much they want to put in or be involved in the wedding. Don't be embarrassed, everyone makes mistakes, and you have a beautiful daughter and a new son in law who are simply having second thoughts about how they handled it. You can "unmarry" them, but it's ok to give her a shower. As long as everyone is clear that this is "after the fact", then it's really up to them if they want to come, and/or give a shower gift. I'm sure many people will be glad to support her, even now and if not, they certainly do not have to participate. Technically she probably should not wear a traditional dress, or have the pomp typical of a first wedding, but truthfully if this is what she wants, who can tell her no? I would not say anything about bringing or not bringing gifts. People can make their own decision about whether or not they want to bring a gift, even if all you had was a reception. If it were my daughter, I would counsel her about having an all in one event, where they exchange vows and have the reception in the same place/hall/etc. However if a church wedding is extremely important to her, I would probably let her. As you said, this is your only daughter, and its a once in a lifetime chance. Maybe not exactly how you would have wanted it, but at least she's willing to try and make up for it in a way.
I welcome your thoughts, let me know if you want to talk more