I just noticed the same thing while watching this movie tonight. 1939 was the establishment year for St. Stephen's School (for exceptional children?) and for the animal shelter. I didn't notice a third instance. My interpretation is that this was shown to draw a parallel between the way people deal (or don't deal) with unwanted children and pets. Maybe unwanted is a strong word; James Woods character genuinely seems to care about his daughter. But when a child or pet becomes more of a burden than is foreseen, the easy solution is to hand responsibility over to a third party.

1939 is famously known as the "Best year ever for movies." Gone With the Wind, Wizard of Oz, Mr. Smith Goes to Washington, to name a few.

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This is what I got from the site The 80's Rewind Cat's Eye page.
1939 was the year Hubie Marsten hung himself in 'Salem's Lot', and it was the town's big dark dirty secret! He was in fact the source of all the trouble they went through
(Family Guy)There is no Peter, only Zool.

One was the animal shelter
Wenn zwei sich streiten, freut sich der Dritte

also noticed this, but have not found an answer
bump