Relative Clause Removal of "Relative Pronoun"

So I have a grammar book that says you can remove relative pronoun when it is used in defining relative clause, if it is non-defining you can't.

For example:

The man who we met yesterday was a sales representative.

The man we met yesterday was a sales representative.

both correct. But:

My father, who you met yesterday, lives in Germany.

According to the book you can't remove "who" from this sentence. Is this acceptable for all cases or just particular ones?

Solution 1:

The book has it right, except for one further condition: you cannot remove the relative pronoun when it functions as the subject of the relative clause.

So:

The man [who] we met yesterday... - "who" is optional. But

The man who came to see us yesterday... - "who" is required.

Solution 2:

The rule you cite is mostly true, but it's not complete, because just mentioning "relative pronouns" doesn't distinguish between

wh-words like who and which, on the one hand, which can occur with all relative clauses,
and
that, which can occur only on restrictive (integrated, defining) relative clauses,

The man whom we met yesterday was a sales representative.
The man who we met yesterday was a sales representative.
The man that we met yesterday was a sales representative.
The man Ø we met yesterday was a sales representative.

But that can't occur on non-restrictive (supplementary, non-defining) relative clauses,
(in what follows, ungrammatical English sentences are *marked with asterisks)

The chairman, who(m) we met yesterday, was once a sales representative.
The chairman, who we met yesterday, was once a sales representative.
*The chairman, that we met yesterday, was once a sales representative.
*The chairman, Ø we met yesterday, was once a sales representative.

Non-restrictive relative clauses also bar relative pronoun deletion,
as the last ungrammatical sentence shows.

The rule also doesn't distinguish between most relative pronouns and those relative pronouns -- either that or wh-word -- that are the subject of their relative clause. Subject relative pronouns are also immune to deletion; English tensed clauses require a subject, and this requirement overrides.