Adding more batteries to our 5th wheel.
blondee, lets take the easy question first. The TV probably requires 120 volts AC. The batteries provide 12 volts DC. These do not match up, unless you have a gadget called an 'inverter' which takes 12 vdc and produces 120 vac... If you don't have one built in, you can add one to power the whole trailer or just use one to power specific items (like the TV).
Why do the batteries not 'last longer' with more of them? Hard to say, but the first thing I would check is what kind of batteries you have. There a 3 classes of batteries out there. 'Car' or starting batteries are designed to provide a high currrent for a real short time, and always be kept at full charge. They are rated at so many 'cranking amps' and are essentially useless for powering trailers. Then there are the dual purpose batteries which can both start a vehicle and provide stored power, but being a compromise, don't really do either really well. Unfortunately, these often find their way into RVs. The last type, the type you want, is a true deep cycle battery. These are rated in 'amp-hours' and do not have a cranking rating.
If you have good battery types, look at their 'amp-hour' rating. This should give you an idea of how long they will last. If we presume they are all 12 volts, properly connected in parallel, they should provide essentially the sum of their individual currents. (However, for best effectiveness, all the batteries in a bank should be as similar as practical).
Also, check the water level in each battery before charging to ensure that they are not low on water, and then check each battery individually after charging to ensure it is 'good'. A load meter (not a voltage meter) and/or a hygrometer (battery fluid tester) should tell you this.
Note that for longest battery life, don't discharge them more than 50% before recharging them. Also, check that you have a good ('intelligent') charger which usually has 3 'stages' to provide the best charge.
If I couldn't find any obvious problems with the battery bank, I would probably put a current meter in series with the batteries and find out what the average current draw was, and then compute how long the batteries 'should' last at that draw. For instance, lets say the batteries each have a 150 amp-hour rating. With 3 of them, that would be about 450 amp-hours. So if my average current draw is 45 amps, I should expect to get about 10 hours of power. I would monitor the gauge, to see what the reading is at 5 hours, and the start and end of that reading. Then continue to see if it starts getting weak around 10 hours. I would not run them completely empty, and I'd only do this test once.
If my meter did not accurately indicate to me when the '50%' charge level was reached, I'd investigate a better meter.