Well you are right everywhere, nothing wrong ! Except that the meaning of the sentence is supposed to be

Paw-Paw is a veteran, of what Tex is very proud

“dont” actually refers to the fact that Paw-Paw is a veteran; but I agree there is an ambiguity.

You can use both, as both are correct. Tex can be proud of Paw-Paw or of the fact that Paw-Paw is a veteran in french as well as in english.

Now, the comma make me think the probability of the second choice is more likely because it separate “The fact that Paw-Paw is a veteran” from the second part of the sentence. But then one could ask : Why is Tex proud of the accomplishement of someone else ? Honestly, these are considerations outside of the understanding of “ce dont” and “dont”, and you’d need to have some context or the will to split hairs to settle this.