ini wrote in linguaphiles

German possessives

Why can I say

(1) Das ist dem Peter sein Auto.

but not

(2) *Das ist dem Peter dessen Auto.?

I've read a lot of argumentations about why the personal pronoun turns possessive but not a convincing one why (2) isn't well-formed. Does it have anything to do with case assignment (insofar as case assignment might not work with a demonstrative — but that's just a stab in the dark)?