The Scottish Tory leader was on the winning side of the 2014 Scottish independence referendum when the country voted to stay in the UK, but backed Remain when the UK voted for Brexit in 2016.
And Ms Davidson, speaking in a podcast organised by finance giants Brewin Dolphin, voiced fears the SNP is using the Brexit vote to agitate for independence.
She said: “The vote in this referendum, in the Brexit referendum, was: what was the UK going to do? People like myself and my parents voted to remain, but not so Nicola Sturgeon could hijack the vote for something else. And that really muddied the waters in Scotland.
“So, there’s quite a lot of people from different political parties who have found their voting intentions slightly skewed when they voted on a single constitutional issue … it’s a much more mixed picture than that.
“But I have to say, as someone who has fought two constitutional referenda now … I’ve won one and lost one … but I would happily never fight another constitutional referendum again in my lifetime. And I would happily never fight any binary referendum because I think it pushes people into camps.
“I think the bitterness you’ve seen, both in Scotland after the independence vote and we’re now beginning to see in the rest of UK after the Brexit vote, shows the aftermath of a referendum seems to be much angrier and scratchier than the debate that leads up to it.
“I think the divisions are really unhealthy in politics right now.”
The Tory leader recently announced she is pregnant, with her baby due in October.
And despite the Tories falling behind Labour north of the border in recent polls, Ms Davidson insists she still has her sights set on becoming First Minister after returning from maternity leave next spring.
Ms Davidson said: “I’ve always said my ambition beyond the job that I have is to become the First Minister of Scotland.
“I think I’m unique in that I’m the only person I can think of in recent politics that is the constituency representative for their opponent – Bute House is in my patch, so I’m Nicola Sturgeon’s MSP.
“But I’d quite like to swap roles, so rather than being the MSP for Bute House I’d like to be the MSP in Bute House. Once I come back from having my first child, let’s see where that takes us.”