Once somebody is in (say a parent without a child) can they open the door from the inside to let others through (say another parent with several children in tow)?
As this is a lap-pool associated with a gym, I can see how an argument might be made that this is a pool for serious training and not a recreational pool or designed for children. However, I would counter that with 1) Some children could be training seriously, eg. for school or other competitions, 2) Children’s water play is important for learning water safety and could lead to a sporting and general fitness interest in swimming, 3) Children are residents too, with a right to use and enjoyment of the common property.
A fear from serious users of a training pool might be that they won’t be able to use it because it is full of kids. A reasonable solution would be to have designated, child-friendly times for recreational use and other times designated for training, perhaps with a booking system.