Heating my kids pool - physics question.

[HavocXphere]

you dont need a massive pump, take this into consideration : you have for arguments sake 2L of water in the pipe eading for the roof ,2L = 2kg , and you have 2L in the pipe coming back down,2L=2kg ,its balanced until you add something to tip the balance one way ie:your pump . i would even say a slower pump is better as the water has more time to heat up in your pipe.
hope this helped

Once its rolling its balanced. The issue is getting to that point. At startup it needs to push X L up without a counterbalance.

I also suspect it'll be more than 2L even with hose pipe diameter.