You can hook both chargers to one bank of batteries
so long as you have it on the correct side of the combiner or isolator. This way either charger can be used to charge both banks in case you have a charger failure. Generally, you would connect the chargers to the house bank. The house bank then charges the start bank via the combiner or isolator. This way makes it pretty much automatic meaning you don't have to mess with switches in order to keep both banks topped up. You will still have those switches to bypass the combiner or isolator if they fail.
You can put two or more sources of DC to a bank of batteries
. Don't worry about that.