Meaning – What Does ‘Snug on That Perch’ Mean?

The that here is not subordinating, but adjectival.

the third criterion for causal studies, that of controlling

is the same as

the third criterion for causal studies, that [criterion] of controlling

or

the third criterion for causal studies, [the criterion] of controlling

or

the third criterion for causal studies, [i.e. the criterion] of controlling

So, what the sentence says, is

1. It is very difficult to meet the third criterion.
2. The third criterion is "controlling for all other potential influences".

what with relatives and everything

could also be written as:

what with relatives and all

It means: Considering relatives and others that they know, each person being acknowledged are expected to result in sales of more than one book.
This is a common view when low sales are anticipated. Direct sales might be low, but they may talk others into buying.