Well, I don't think you can use the argument of safety at all for this gig.
The whole tour is at arena venues and the majority of tickets are seated. And its the type of venue that it is safe to stand at any age, provided you aren't right at the front.
I'm assuming you are thinking of going to the Manchester gig (as its the only date in November). If its one of the other venues, they are pretty similar anyway.
In terms of noise levels, I don't see it being a problem, especially if you are in the seated areas. The acoustics are really good at the arena so they don't need to turn it up to 11 in there.
I know loads of people who have taken kids of a similar age to gigs, with no problem at all. There is no age limit at the venue; it would be up to the band to impose one and Muse just wouldn't do that. They are a pretty good bet for a family first gig in terms of the audience they draw.
Curfew for the Arena is generally 10.30pm - 11pm. (depends on the gig, but in recent years its tended to be 10.30 rather than 11 to allow people to get public transport home). They would be onstage 9pm to 9.30pm.
Your DW is being a little bit over protective imho. Its one night, I'm sure they could cope even if it is a school night.
I suspect its just because she wants to go without the kids though...