Well first your charge controller needs to be matched to your battery. If this is the same system you had before, you should be fine with swapping back in the long life sealed battery. What you can't do is swap in an even bigger battery - such as connecting two of those batteries in parallel - because while the pump would run for twice as long, the charge controller would either blow an internal fuse or self destruct trying to recharge the now twice as big battery.
Charging the battery off of the car alternator is not going to really work. Again its back to the charge controller. The alternator in the car is designed to recharge CAR batteries (low capacity - high output) not long life (high capacity - low output) batteries. I'm not saying it won't charge at all, but it would take forever and it would not be good for the batteries or the chargers.
You could design yourself an A-B switch and switch between the two sealed batteries. That way only one would be connected to the pump and controller at any one time. You would have to remember to switch it once a month to keep the batteries charged up AND in an emergency you would have to manually switch between the two. (Remember you are dealing with low voltage but high current so you need heavy gauge wire and an appropriate switch, but this is standard stuff at a marine supply store.) But of course once both batteries were out of juice you would be out of luck. Personally I'd just go with the single battery and put the money toward a quality inverter type generator so I could have some lights and run my pump and charger during long outages (Oh and charge controllers generally HATE cheap big box store generators and will produce little or no charging power for your batteries when connected to one so if you go the generator route and want the battery to charge (you could always just assume that the pump will run off a cheap generator from that point until power is restored and skip the inverter generator) you'll be looking at a generator that costs 50% more for the same wattage as you see in the big box stores.)