Does Wyoming permit primary cross-over voting?
Yes. From Ballotpedia:
Wyoming law stipulates that parties conduct open primaries for congressional and state-level offices. While a voter must be affiliated with a political party in order to participate in its primary election, any voter, regardless of previous partisan affiliation, may change his or her affiliation on the day of the primary.
She will win the primary because the uniparty will make it so. I would bet the farm on that. And republicans ought to refuse to vote for her in the general election, let her lose the seat to a dem. She is a a liar and a cancer on the body politic. She MUST be defeated.