The Mystery Cartoon Character Game, ongoing-ier.

"Thinking quickly ..." This has Commander McBragg written all over it: he's been all over the world, in countless dire situations, yet emerges unscathed simply by refusing to panic.

Nope, it is not Commander McBragg at all.

I truly have no idea, and thought I had it, but I don't.

4. A bunch of dogs on hot on my trail.
5. Only one of them is polite enough to knock and ask if he can catch me.
6. While I am not the main character of this short, the focus is mostly on me.

I've concluded it's an English fox, but I can't find one that matches every single clue.

It's Reginald Fox from Out-Foxed.

Yes, Saltyboot, it's Reginald Fox from "Out-Foxed."

1. When one of the hunting hounds appears outside of Reginald's home, Reginald calmly tells the audience: "Ladies and gentlemen, fear not for my safety. After all, I am smart as a fox you know."
2. Unlike most cartoon foxes who act like con-artists, Reginald is a very polite gentleman of a fox.
3. Self-explanatory.
4. The hounds are after Reginald because of a fox hunt.
5. Droopy is the only one who actually knocks on the door and politely asks Reginald if he can get in his sack.
6. "Out-Foxed" is a Droopy short. However, most of the cartoon focuses on Reginald outsmarting the hounds on his tail.

Thanks, and now..... here's mine.

I am the main character's best friend.
I am known for loving rum.
We were in comics before we were animated.

That could be anyone. I'll have to look it up.

It might be Tintin's friend Captain Haddock.

That's it peterhale, it's Captain Haddock the rum loving friend of Tintin.

Take it away.

I dimly remember watching "Hergé's Adventures of Tintin" on the BBC in 1959 - an English-dubbed version of the 1957 Belvision series. They were serialised in 5-minute episodes. Very limited animation, as I recall, but quite dramatic. I always loved Captain Haddock - a wonderful character!

1) I have to cope with my superior's extremely emotional outbursts.
2) His current worry is that his son is avoiding his responsibilities.
3) I try to tell him that "love at first sight" only happens in fairy tales - but it is happening as I speak!

This is another I'll have to look up.

Perhaps this is Herb Copperbottom from Blue Sky Studios' Robots? Herb works as a dishwasher at a diner where a mob of robots have breakfast, so his harried boss tends to get snappy. Herb's son, Rodney, has big ideas of being an inventor like his idol, Bigweld, but Herb tries to focus the boy ('bot?) on more mundane endeavors. It doesn't help that Rodney gets smitten with the curvy Cappy.

Alas, no - not Herb Copperbottom. The clues are written in the first person, so clue 2 does not refer to the character's son.

4) I nearly get dubbed Sir Shegotaway, until my superior realises what I am saying.
5) When I tell him what he son has vowed, he is delighted - when I point out there might be any number who fulfil the criterion he replies "That's his problem! He's given his word - we'll hold him to it!".
6) I reluctantly set out on a quest throughout the length and breadth of the kingdom.

My thinking cap is securely fastened now. It's the Great Grand Duke, from "Cinderella."

That's my thought too, alas, a bit too busy to answer yesterday morning due to work.

It is indeed the Grand Duke from Disney's 1950 Cinderella (and it's sequels).

1) The Grand Duke is administrator for a very volatile King.
2) The King wants the Prince to settle down and produce heirs.
3) At the Ball the King is disappointed that his plan is not working.

Grand Duke: I did try to warn you, but you, Sire, are incurably romantic. No doubt you saw the whole pretty picture in detail... the young Prince bowing to the assembly. Suddenly, he stops. He Iooks up, for lo! there she stands, the girl of his dreams. Who she is, or whence she came he knows not, nor does he care. But his heart tells him that here, here is the maid predestined to be his bride. A pretty plot for fairytales, Sire, but in real Life... oh, no... no. It was foredoomed to failure!
(As he is speaking, the Prince sees Cinderella, and responds as the dialogue.)
King: Failure, eh? Take a Iook at that, you pompous windbag!​

4) The King is delighted with the success of his plan and is about to knight the Grand Duke, pausing only to ask what title he wants to take. The Grand Duke's response: "Sire, she got away, sir!" strikes the King as an odd choice.
5) While dodging the King's flailing sword, The Grand Duke explains the Prince is in love with the girl:

Grand Duke: The Prince, Sire, swears he'll marry none but the girl who fits this slipper.
King: He said that, did he? Ha-ha! We've got him! Yahoo!​

6) By proclamation of the King:

"It is upon this day decreed that a quest be instituted throughout the length and breadth of our domain. The sole and express purpose of said quest to be as follows: that every single maiden in our beloved kingdom, without privilige or exception, shall try upon her foot this aforementioned slipper of glass. And should one be found upon whose foot said slipper shall properly fit such maiden shall be acclaimed the object of this search and immediately forthwith shall be looked upon as the one and only true love of His Royal Highness, our beloved son and heir, the Noble Prince."​

All yours, Emeraldisle!

Thanks, Pete. Now here's a real good one:

1. I'm a single mother of three--at least until I meet my guy.

2. My offspring are named after a painter, a composer, and a queen, respectively.

3. Aside from others of my kind, my closest friends include a friendly and helpful mouse, and a butler butt-kicking mare.

Duchess the angora cat from Disney's The Aristocats. Her kittens are Toulouse, Berlioz and Marie, all cute as buttons.