Pools can have a multitude of different changing set ups.
I have used a "family changing room" once which was literally a room of benches and pegs for multiple families to change in. Awkward. It was built in the 70s and closed down a few years ago. I didn't rush to go back and use it. The centre we use frequently has a female/ family room so suitable for female carers and mixed sex children up to age 8. Many girls use it solo beyond 8. It's not suitable for male carers who tend to be the minority by a significant margin.
Single sex can have different balances of communal change / cubicles. If there are benches/ pegs and no signage to the contrary, I'm happy to change in that space as I find many cubicals too claustrophobic to enter, and I have no issue with brief functional nudity. I tend to use a poncho towel anyway for warmth and a little discretion.
Mixed sex changing villages don't tend to have space to indicate acceptable communal changing. It's not clear from the OP whether this is the set-up of the family room described. I have occasionally seen families change at the edge of our changing village, they're not supposed to, but they were clearly focusing on the practicalities of changing not exhibiting around so I've just ignored them.
Without knowing the exact set-up of the family room, it's hard to call if it's unreasonable to not use a cubicle. I found a closed room easier for dealing with young children, I didn't fancy my houdini toddler DS2 slithering under cubicles while I was in a state of undress!
All I can gauge from the OP is that for the age structure of her family, the single sex facilities are appropriate if the family room isn't to their taste.
The pool we have lessons at is great for a range of changing options, but having a 9yo DS with dyspraxia and ASD, and a 6 yo who needs constant supervision, we're left with 3 larger cubicals in the complex as the only option short of getting a radar key to use the disabled facility, as DS1 often needs the support and is beyond independently changing at the end of the day. Single sex facilities are no longer an option for us for the time being. I'd be a bit cheesed off if I'm having to wait around getting cold while a capable 12yo and his dad are unnecessarily using the limited facilities that we can use when they have other options.