Why did my generator trip the feed breaker in the subpanel?
Frame challenge:
You need a generator interlock. Full stop.
You need a mechanical device that positively ensures the generator cannot backfeed the power grid.
You cannot replace this with a checklist, or with &quot;being super smart&quot;. The rest of us need to do that, and you are not smarter than the rest of us - especially not during a power failure when you're running around trying to get the lights back on, in the dark, in the rain.
If you doubt that, consider the difficulty you're having solving this problem, in good conditions. You are not Superman and you CAN make mistakes.  The interlock's job is to ensure those mistakes don't kill someone. And it is mandatory.
So the idea of backfeeding your pool subpanel is Right Out, because it makes the proper interlock impossible.  You are either going to have to
a) lay a new cable, or
b) &quot;permanently&quot; re-task the pool supply cable to be the generator supply cable, resulting in the pool ONLY being powerable off the generator.
Yes, I'm aware that's exactly what you're trying to avoid.  The rest of us don't get to do that, neither do you.
I say &quot;permanently&quot; because there is nothing wrong with doing permanent and proper wiring seasonally, as long as it is proper and to Code.
Now, if you get us some information about your main panel, we can guide you to some good choices in generator interlock. (We're not normally a shopping site, but we can give some guidance).
Why?
Because power flows both ways, as you well know from your efforts to backfeed the pool sub.  It also backfeeds out onto the neighborhood grid.  It also backfeeds through transformers.  When you energize the 120/240V side of a 120/240--9600V transformer, the high side of the transformer energizes at -- anyone, anyone, Bueller?  Correct, 9600 volts.
And that's how you kill linemen with a Harbor Freight generator.