Correct. (If they indeed have a temple wedding...obviously not all have it @ the temple...and some try to do a "twin billing" @ dual locations to accommodate non-Mormons)
How about the reception, I'd be paying for, could I go to that?
Receptions @ other locales.
Would she and her new husband both have to have the temple recommend?
Yes. (For a temple wedding)
I've seen one article from a speaker @ BYU-Idaho who heavily stressed to Lds young adults NOT to seek temple recommends, especially for say, the wedding of a sibling.
The Mormon church, he said, essentially liked to keep such temple recommends of young adults in reserve for those either going on a mission or getting married.
Hence, it's more subtle pressure upon Lds young adults to do one of those two things during their college years.
Actually, here's the quote: From Elder David E. Sorensen, Jan. 13, 2004:
... The privilege of receiving one’s temple endowment is a serious matter...We are concerned...an increasing number of young adults 18 years of age and older are obtaining temple recommends from their priesthood leaders to receive their...endowment without the immediate prospect of temple marriage or full-time missionary service. Single members in their late teens or early twenties who have not received a mission call or who are not engaged to be married in the temple should not be recommended to the temple for their own endowment. They can, however, receive a limited use recommend to perform baptisms for the dead. The desire to witness temple marriages of siblings or friends is not sufficient reason to recommend one for a temple endowment.
Source: BYU-Idaho devotional presentation Agency, Priesthood, and Black Powder
All, lurkers: Yet another reason to NOT consider the Mormon church; or, to leave it.
Two part question/answer.
1. She could marry him as a non-mormon and have a wedding performed at the local church by clergy with those invited in attendance regardless of temple recommend.
2. She would have to convert to mormonism and in about a year qualify for the recommend in order to have a temple wedding. Those without a temple recommend would be barred from attending in the temple.
"How about the reception, I'd be paying for, could I go to that?"
Yes, as that is usually held at a local ward or stake bldg. and is open to those invited.
"Would she and her new husband both have to have the temple recommend?"
For a temple wedding, yes.