So how would I wire this?
I had a similar situation once but was using Lithium batteries, but my solution should work with lead acid as well if the chargers you are using have a smart current based charging algo.
It requires two 12 volt chargers, with isolated secondary circuits. Isolated meaning that neither of the output wires is connected to anything else including the ground line in the power cord.
Then it's really simple: charge one battery with one of the chargers and the other battery with the other charger. You do not need to disconnect the batteries.
Yes I know this means the chargers are connected in series as well, but the charging current for each battery is still controlled by each charger....more or less. In your case if you switch off the power before charging then the current is exactly controlled by each charger. If you leave the robot powered, then I'm not sure the current is 100% deterministic.
When I used this method, the robot remained powered while charging and I never had any issue, but I had checked the chargers for noise prior to using them and found the output very quiet. And just to be sure I didn't burn the house down I had thermal fuses sandwiched between the batteries. Since you're using lead acid the risk of fire due to overcharging/uncontrolled charging is very low.