Cheney was not Reagan in any way. Dick Cheney, her father, HATED Reagan.
Based on what evidence?
He gave Reagan's eulogy.
In his diary, President Reagan recorded his pleasure in Cheney's defense of the administration, and Reagan's press secretary described Cheney as "probably the most effective supporter the President has in the House of Representatives, because he's intelligent and he can support the President without appearing to be following the President blindly."
Reagan was a maverick in the beginning and was opposed by the Establishment. But they learned to live with him and accept him and many came to see themselves as Reaganites. Trump is a maverick now and in that he has some kinship with Reagan. He wasn't able to tame or win over the GOP Establishment and still faces opposition from the elite.
I don't like Cheney either, but facts are facts and ought to take precedence over one's likes and dislikes.