Yes, that's it.
Why it makes you feel strange is perhaps because you speak English. Please take a look at the post @sbkgs4686 has cited for details, but the point is that English (as well as many West European languages) has a word class determiner that you can use only once in each phrase. "That", "the", "a", "any", "my", "their" are its typical members so that you can't use any two or more of them at the same time. As a result, you are forced to make ones like "a friend of mine" or "these cats of hers" instead of something like "*a my friend" or "*these her cats".
Japanese is free from all such things, so you just put:
あなたのその息子 "your that son": that son of yours
彼女のこの猫たち "her these cats": these cats of hers
For "those trash of his" I can think of multiple situations which I don't think literal translation works very well anyways.
What also should be noted is that the default position of この／その／あの is after possessive, before ordinary adjectives if any: 私のこのかわいい猫たち.
Oh, by the way, pronouns are just nouns in Japanese, that means:
美しい日本の私 *beautiful Japan's me → "Japan, the Beautiful, and Myself"