What is the difference between two sentences...
My uncle has three sons all of whom work in the same office.
My uncle has three sons they all work in the same office.
In the last sentence, is there any grammatical mistake regarding joining two clauses?
And in my first sentence, why can't I use all of them?
The second example is a splice of two sentences. It would be common punctuation error for native speakers to write this with a comma after "sons".
In fact these are two sentences. You should either put a full stop after "sons", or a semicolon.
My uncle has three sons; they all work in the same office.
Alternatively, you can link with a conjunction:
My uncle has three sons, and they all work in the same office.
Now, using "all of them" would make the second part a complete sentence.
My uncle has three sons. All of them work in the same office.
But "all of whom work..." is not complete (the word "whom" is acting as a relative pronoun) so this is not a complete sentence. You could, optionally, put a comma after "sons".
Compare one sentence with relative clause, with two sentences:
This is an apple, which has a hole.
This is an apple. It has a hole.
This is an apple, and it has a hole.
