I don't have any suggestions regarding the solenoid issue specifically, but with two 12-volt batteries in parallel and one is replaced, it is always best to replace BOTH batteries. Both batteries must be identical as much as possible in type and in age. If one battery is "weak" it will soon have an effect on the new battery and you might end up with two bad batteries (again).
By the way, unless you measure voltage on EACH of the two batteries with them disconnected from each other, you won't be able to know if one or the other battery is weak. And measuring voltage (or assuming) after a fresh recharge doesn't tell the whole story. Best to use a hydrometer and/or a load check meter to learn if the battery needs to be replaced.
If you already know all of this; sorry but maybe it would help someone else also.