I searched "genetic recombination" on nsdl.org and then did ctrl+F, typed in animation, and looked at all the videos that had "animation" in their description.
For all the youtube ones I started by searching "genetic engineering" and "genetic engineering animation." I also searched "genetic recombination" and didnt find anything. "gene therapy" came up as a related search, so then I searched those words and found this one.
Source - Dolan DNA Learning Center - DNA From the Beginning
2D animation with textual narration by scientists proceding through a long series of steps
Audience - Intermediate
Searched biosciednet.org for 'genetic recombination'
Source - Dolan DNA Learning Center - Genes to Cognition
2D animation with narration in a series of steps
Audience - Advanced
Searched biosciednet.org for 'genetic recombination'
Cool animation on the evolution of the Y chromosome, but not really related to genetic engineering. Probably came up because of the 'recombination' events between the X and Y chromosomes.