Now the question was, could you fork (especially a PoW blockchain) a blockchain and have it run parallel for a while and then reunite them?
What you're referring to is a blockchain reorganisation.
There can only be one chain and one chain will be orphaned with its blocks so there will be one transaction history.
A reorg can only happen with compatible blockchains following the same consensus rules (eg when 2 miners find the solution to the same block, one of the blocks is eventually invalidated to favor the one with the highest difficulty sum/POW)
For example, BCash won't reorg to Bitcoin even though the bitcoin core has more proof of work because they aren't compatible/follow different consensus rules: Bcash's genesis block, 478559, has to be greater than 1MB and bitcoin can't fulfill that rule so to BCash nodes, the Bitcoin chain is invalid.