I personally can't stand gyms but I can see the main benefit is that you can go there pretty much any time and you can do a 30minute thing and be done with it. With your choice, I reckon $10 for pool membership is prolly better value, presuming you can sneak the kids in and your brain doesn't melt after a couple laps.
As an argument for just ride more ... I do a bit of circle work at a reserve near me ... basically it is linking together a bunch of garden beds and skirting around a soccer field. I do it like a series of sprints sometimes on my DH, sometimes on my XC etc etc. Think of it as a series of corners which I try and hammer as hard and as drifting as I possibly can ... which then leads to the straights around the soccer pitch which again I try and hammer as hard as I can. All up I last maybe 15 to 30mins and I'm absolutely shagged.
At my peak I was doing a couple laps flat out, prolly 400m at most per lap, a few times an arvo to escape the kids
You do tend to look a bit odd riding around in circles, sometimes giggling madly whilst picking yourself up off the ground after blowing a corner and crashing your brains out, but frack it. I've had some awesome sunsets over my track, definite fitness and skills improvement and more saddle time, all for nix and minutes from the house and family. Doesn't take much ... just need to be creative about where you do your circle work