Which process occurred frequently in the early history of the three domains on earth, and makes determining phylogenetic relationships of that time difficult?

The answer is horizontal gene transfer.

Horizontal gene transfer enables gene flow between genomes of two organisms. It is a common process between different species of prokaryotes and even, between prokaryotes and eukaryotes. When trying to reconstruct evolution and phylogenetic relationship, scientists face some difficulties because they cannot say the common gene transfer with the horizontal one.