I don't really see the problem. I always thought this was how these things were supposed to go. I would much rather be relieved of duty than have some player casting daggers in my back while I ran the game. It doesn't seem they were passive aggressive or deceptive or anything. They simply intend to get their game on, and when you didn't provide it, they moved on. They even invited you to attend as a player when you can. Frankly, to me this is all an example of players doing it right.
In addition, I'd say that it *is* a reflection on your DMing skills. Their action is a pretty clear statement against your game. After all, if they felt positive, they'd still be eagerly eating it up. Honestly, even if they came onto the board an protested my characterization (by saying something like "It wasn't a negative statement about Achan; it was a positive statement about DM #2!") I'd still say that it comes out pretty bad for you by way of comparison. To me, that makes this a lesson to learn from. You now have good feedback: you weren't running up to snuff, and you'll need to get introspective about how to do better. Frankly, I think you're lucky to get such an unambiguous message.
On a smaller scale, reading of your frustration that you canceled due to weather and they continued anyway tells me a little of why they might have installed another DM. To me, your phrasing reveals at least a little bit of a control problem -- like if you call it off, they better honor that! But that's not your place. And maybe they are picking up on a style that doesn't sit well, and opting out.
For my part, I've been in the same position on both sides. I've recently begun running a once-a-month game, and by the second game the players were talking about rotating DMs or "deciding who will run it long term" -- when I was already in place and assumed it was fait accompli! My response? Here is what I wrote on our private forum:
aboyd said:
player said:
And, we need to figure out who will DM - do we want to rotate?
I'm up for anything, with one exception. I really prefer that we start low-level. So I'll play or DM, but I'd want to stick with the level 2 characters we've already done.
In other words, I made it a non-issue by being willing to do whatever worked.