I hope it goes well.
If it was me I would go for a one on one sit down with someone then.
One person she can be comfortable with.
I will just be honest and say I don't think she can handle a press conference on her own. If there is even a moderate turn out and reporters actually start in on questioning her (Nancy is filtering question because she wants her to come back). If she has done as poorly communicating what she wants to say in a friendly environment, this could have the complete opposite effect you think it will.
I will kindly suggest that because you know her and know what she is trying to say you cannot see how she comes across, and because you have faith in her and believe her you are over estimating her abilities in this type of a situation.
Keep in mind you have no idea what someone may have dug up that they can't confirm enough to print but they can absolutely blindside her with a question in a press conference she invited them to.
Just make sure you are considering other angles than "Billie just needs to tell everyone what happened over a 72 hour period over a month ago and then things will be better and everyone can stop being suspicious of her".
Of all the possible outcomes that is the least likely even if she does well. The suspicious train has sailed. She needs to stop worrying about what people think of her, they already think it, ship sailed, let it go.
If your goal is to get the focus off Billie and on to Haley put Billie in front of the cameras to make more documented contradictions (some people just don't communicate well, doesn't make them evil, just makes them the wrong person for the job) is not going to do that.
imoo..... good luck