I would do something similar to your dh, except that I would probably skip the family meeting bit and go straight to doing a fun, kid-approved activity that starts *before* TV time and goes straight through it, hoping that in the moment they forget about their show. When they *do* realize they missed it, then I'd do a straightforward explanation about why the change, asking for input about how to make it work best for them, while being firm about the basic no more second show time.
With my dc, I'd tell them about my schedule, why I think it's a good thing for all of us, and how it just doesn't work with the second tv time. I'd emphasize they still get the first time, and I'd be open to modifing my schedule in whatever ways both worked for the kids *and* for my goals in making the schedule in the first place. If it were an acceptable option, I'd suggest they tape the show and watch it at a better time, because that's pretty win-win. If that's not an acceptable option, I'd be ready to explain why, because my dc would almost certainly suggest it right off.
And yeah, I'd be ready to reflect and validate their upsetness while still holding firm to my belief that this new schedule is worth it - that it is better for everyone, or is flat out necessary, or whatever reason I have that I am going to do this. I would also make a strong effort to work with them to find ways to make the change at least palatable for them, if not pleasing, listening to them and making any and all changes they suggest that wouldn't mess up the whole point for the schedule change. But kids sometimes get stuck on one option, and if they refused to accept anything other than the previous status quo, then, well, either it's worth it or not.
I *do* change my mind in the moment if I realize that it's not worth it after all - because often it isn't
. Yes, it lets my kids know that I will change things if they are upset enough, but I don't think that's a *bad* message to send at all. Because I care about their welfare, and that means respecting their views and taking them into consideration as much as possible. And I think that evidence that I am willing to work with them in most things most of the time helps in the times when I decide, after consideration, to *not* change course even when they are very upset. It certainly helps *me* to retain the courage of my convictions anyway.
Any of that help?