I have the DNA (via Ancestry DNA) of a mother and 3 of her children, one son and two daughters. I know I can get an approximation of the father's Y-chromosome from his son. Is there a tool to generate an approximation of the father's autosomal DNA from this data? FWIW, I also have the DNA of two of his siblings. All siblings in this sample are full siblings.
There is the Lazarus Tool on GEDMatch.com that is available to Tier 1 members of Gedmatch. Tier 1 means you have contributed at least $10 to GEDMATCH for the current period.
You can upload your families Ancestry.com/23andMe/FamilyTreeDNA results to GEDMATCH and then you can use the Lazarus tool to reconstruct a pseudo-kit for a untested / deceased individual to get a partial Autosomal DNA kit.
It can even be used beyond your parents but in theory a couple of generations away by capturing multiple descendants from different lines.. it will not of course be a complete kit but capture common elements from the included kits.
The minimum is at least 2 direct individuals that are in the children / grand-children range (referred to as Group 1) and contain up to 11 individuals kits and then further generations (group 2) is made up of more distant relations of siblings and cousins of the individual up to 100 kits.
The constructed pseudo-kit can then be utilized as a baseline comparison as a 'common ancestor'.
For more information you can also look into the GEDMatch Lazarus forum (you must be logged into GEDMatch).
Kitty Cooper also posted a blog posting (Jan 2015) "Putting Humpty Dumpty Back Together Again" discussing the use of the tool.
On the Y-Chromosome comment in your question; between a father and son the difference should be extremely negligible (at most 1 chromosome difference) as the Y-DNA markers do not mutate that quickly and even over hundreds of years may only be a few markers off and thus the power of the Y-STR testing. The Y-SNP BigY tests A LOT (million+) more markers which will result in likely some more differences.