You're gonna want to think in terms of "The Wizard of Oz" here...is your witch a good witch or a bad witch?.....my witch is a good witch, of course...:)....the same is true for dogs and cats and the like....but you're right it IS redundant however in spoken form it's what we do, generally speaking...
Is my understanding here correct?
This sentence emphasizes the fact that -my- dogs are good animals (but not your dogs), while the sentence "hundene mine er gode dyr" is a more generic statement?
I'm trying to get a feel for when to put the possessive pronoun before the noun vs. after it.
In spoken language the emphasis of the ownership depends on how the sentence is said. If the possessive is stressed, then the ownership is stressed, regardless of its placement relative to the noun. In some cases the placement will depend on dialect, and on what sounds better in the sentence. We like our sentences to flow well.
In written language the reader doesn't know which word we mean to stress, so the general rule is that placing the possessive in front of the noun puts emphasis on the ownership - if that makes sense in the setting. This holds true for most physical objects, but gets a bit unreliable with some abstract objects - maybe because the concept of ownership gets less clear when it comes to something that isn't tangible.
For family and pets (like in this sentence) putting the possessive before the noun is very common both in speech and in writing, and I wouldn't read anything into it unless I had context that would indicate that they meant to stress the ownership.
When you throw an adjective into the mix, there is a stronger tendency towards placing the possessive first, simply because it saves us a word:
"Min yngste sønn"
"Den yngste sønnen min"