Could be an overload
This is a 240V (2-pole) breaker. Given the 20A size, it is perfectly legal for it to feed both 120V and 240V loads, and I suspect the pool pump is a 240V load.
A 20A 240V/2-pole breaker has two poles (legs) of 20A each.
A 120V load can draw off one leg and neutral, and it will draw the amps it says.
A 240V load will draw off both legs at once and will draw the amps it says.
So for instance, your pool pump draws 10A from L1 and 10A from L2.
Your washer draws 20A from L1. Let's add em p.
- L1: 10A pool pump. 20A washer. Total 30A
- L2: 10A pool pump. Total 10A.
30A is more than 20A. Whoops!
Or, it could be a ground fault problem
That particular breaker is a GFCI (Ground Fault Circuit Interruptor) breaker. It is looking out for ground faults, which is leakage from the places power is supposed to be, to places power is not supposed to be.
Such leakage is exceedingly common with electrical machines that handle water.
It can also happen in wiring, particularly outdoor wiring.
If you are getting trips when the washing machine is not running, this is likely the problem.
You would need to eliminate one appliance at a time by unhooking all of its wires (hot(s) AND neutral) from the system. You must unhook neutral or the test will be invalid. You don't need to unhook safety ground. If you unhook an appliance and the problem goes away, that appliance is faulty.