How long is the soccer session?
I'm curious to see their policies on scheduling. Having been there, done that with my stepson, I'm guessing that there was probably a disclaimer somewhere on the site or in the paperwork.
Is it club/competitive soccer? What exactly is an independent sports company? I've not heard that term before. Personally, I think that anything other than recreational "for fun" sports & activities are a waste for kids that age. I hope you didn't pay that much for the classes. Also, for that age group, the class are *usually* just for fun, and the kids will be grouped together. It's normal. I don't think anyone's going to get mowed down. They're little kids.
The thing about team sports is that things change in the blink of an eye & parents have to learn to be adaptable - locations change, times change, coaches change, positions change, etc. It's still annoying, but part of the deal.
No, you are not the only parent juggling more than one activity for your kids, but I'd venture to guess that *most* people wouldn't plan both activities for the same day. It's too risky & tiring for the kids. I personally, would never have signed my kids up for 2 physical activities in the same day. It's asking for trouble.
Why can't you switch the day or time of the swimming lessons until the soccer is over & be done with it? The soccer season probably isn't that long, and is temporary. It sounds like the swimming is more of a permanent "must have" fixture in their lives. Or, take a break from the swimming & do the soccer. Your kids might appreciate trying something else for a bit.
That is, unless, you feel like getting into trying to get a refund with this soccer place. It really depends on how much energy you feel like putting into that. For me, it would be a no brainer, personally.
Good luck, whatever you decide.