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.
If my daughter became a Mormon and married in the Temple, I wouldn’t want to go. Nothing against it but I don’t want to go where I’m not welcome.
Plus drinking in the parking lot of the temple is probably frowned upon.
open bar for the reception?? :D