Our pool/swimming school doesn't have any signs indicating what ages can go into the opposite toilets/changerooms. Neither is there a family room, and the shower cubicles don't really offer much more room than the shower. The options are either to change them in the general pool area in front of everyone or change them in the changerooms.

Not sure I'd be comfortable with sending a six year old in to the men's changerooms on his own either, albeit as it's learn-to-swim, the changerooms are generally only filled with dads and kids (ditto, the women's is pretty much just mums and kids). Members of the general public use separate facilities outside the learn-to-swim building.

Yeah, this is a tough one. You want to be able to keep an eye on your child and assist them to get dry/changed etc ... but you don't want to cause anyone to be uncomfortable etc.