add 2nd battery

I would add that when you do buy 2 new batteries, that you make sure that you wire them correctly by putting the positive lead to the coach on one battery and the negative lead on the other battery. If you put both leads on the same battery, the pair will not share the load equally, leading to premature aging of both batteries. This is because even though the jumpers between them are short and very low resistance, they will still add a little to the circuit, and this is enough to be a problem.

Thanks for the help!!! The present battery is 4 years old, so I think I will replace it. I need to figure out if my converter is Li compatible.

being that it is 4 years old already, I will say no.  acid battery should be all relatively the same age.  if it was 6 months old I would say go for it but not 4 years. how long will that battery last right now if you stop for the night with out power keeping your fridge running? 

depending on the answer to the last question I would recommend for you is either upgrading to a better battery, either 6V deep cycles or LiFePO4.  so deep cycles 6V you can get down there from sams club or Costco for what 89 bucks each, but I found a 232 HA US battery for 159.00US.  that will give you double what you have now for power, LiFePO4 is a bit more expensive than bargain batteries, but that's because they are not bargain batteries, kind of compare them to higher end deep cycle batteries.  the price of them has come down quite a lot, as low as 139.00 each I have seen people posting from the US for ones that are good.  I found wattcycle (decently built LiFePO4 battery) for 159.00 on sale.   the missing component is if your converter is Li compatible.

now what is the difference between the two 6V and the two LiFePO4, the 6V will give you about 208AH (231 if you get the US battery I mentioned above) but to get any decent life out of them you only want to use about 1/2 of that so that leaves you about 105Ah (115 for the US battery) and some where around there your inverter will start going into low voltage alarms if you have to much draw also.  with the lithium, the watt cycles are rated at 5000 cycles at 100% depth of discharge so at 5000 cycles even if you drain them twice a weekend every weekend of the year it will out last 99% of us.  so if taken care of that's the last batteries you will have to buy most likely.  so what you get is 200AH you can use for the same price as the US battery deep cycles.  also because of the way the voltage works on the LiFePO4 it probably won't make your inverter alarm until its down to about 10% so lets say in reality you will get about 180Ah from the LiFePO4.  I only use mine down to 10% as that's about where the voltage drops below 12V.  

so its a decision, go cheep and spend 170ish on two cheep deep cycle, spend a little more and spend 320 on good deep cycles, or buy one LiFePO4 wattcycle battery on sale for 160 now if your converter is compatible, as that will give you twice the capacity you can properly use now, then in a few months buy another one, or just spend the 320 and get two at the same price of the US batteries.  

How old is the existing battery? If it's the original battery, 4 years old or potentially older, I wouldn't. Adding a new battery in parallel to an old battery is not a good idea. This is because the new battery will have a different charge capacity or internal resistance compared to the old battery, which can cause uneven discharge and charging rates between the batteries and/or it can lessen the life of the new battery as it tries to equalize them.