.There was a story that Zoe 'stormed out' of an awards show because Mark said something like 'let's not forget this is for Gaby Roslin too' but they always claimed it was tabloid nonsense.
Yes, that was the story that I remember faithfully cutting out of the papers, and then sent it for consideration for Morning Glory. In fact the awards ceremony was the TRIC Awards and if anything it illustrates what a waste of time the TRIC Awards are because the show was absolutely dreadful at that point and shouldn't have been winning awards for anything. But I'm thinking, yes, it probably was because Mark liked Gaby a lot and just didn't think Zoe was up to it. I do remember, after they'd had that very, very long break from working with each other, the first week they were back together there was a live wedding in the house and they did a trailer involving Mark and Zoe getting married, which I assumed was some sort of joke on behalf of the production team.
I don't think it was professional jealousy from Mark at Zoe being the big star, because I think he was just delighted to still be on the show. I remember when Zoe arrived, she was on the front page of Sky magazine (remember that, unrelated to Sky TV, the unisex youth magazine) but Mark was also interviewed in a box-out in the article and he talked about how six months before that he assumed he was on his way out, but now he was pleased to be part of the new team.
As you say, Zoe said she didn't think the producers knew what they wanted, whether they wanted her to be just the same as Gaby or a new young presenter, and she said they used to keep messing with her hair and making her wear suits (like in that clip) which she didn't like. In fact it's amazing how few people remember she even did The Big Breakfast.
There was another moment during the era which I vividly remember but nobody else appeared to even see, which was when Mark threw to another item but his mike was still live because you could clearly hear him shout "Oh, you f*cking idiot" at someone. But there was no apology or anything, presumably nobody was that bothered about the show at that point.