If you use your 12v thermo electric cooler, assuming you started with a fully charged 100Ah battery, it will be 50% depleted in about 8 hours.
So you are stuck with Ice and a cooler, or Ice in that thermoelectric cooler, and ony plugging it in while you actually drive.
Othewise your loads should be handled by 100Ah AGM. By the way there are Gel batteries, and there are AGM batteries, but there are not Gel/AGM. I hope Renogy is not marketing such Unicorn tears.
100 watts will likely prove inadequate, especially portable as they only work when you set them up. 100 watts permanently mounted on the roof would harvest much more energy.
For comparison, I have a pretty refined system. My loads are this 90 watt (max) laptop, my 12v compressor fridge( extra insulated, well ventilated) computer fans LED lights and a TV, with 200 watts of solar on a 90AH high$$ Northstar AGM battery. The battery is my ONLY battery, for house and engine turns 4 years old in Novemeber has over 550 deep cycles on it, and still performs well.
BUt My alternator can always recharge the battery as fast as possible as I control the electrical pressure( voltage), and I have a 40 amp plug in charger which can also basically charge the battery as fast as possible. HIgher ampergae might shave off 20 minutes total from the minimum 6.5 hours from 50%. My solar panels are controlled by a programable MPPT controller.
Your first battery is likely doomed to early failure as your recharging is not really enough, and we also do not know how much you will use the laptop, nor the fans and at what speed the fans will run which will have huge effects on battery capacity and recharging capacity required.
While my laptop can draw 90 watts, it averages about 35 when its battery is fully charged. My laptop basically uses 3x more electricity as my 12v compressor fridge would in an hour period.
The topic of living on 12v is pretty convoluted and there is lot to learn to maximize battery life, but don;t get overwhelmed. Less than ideal just means replacing the battery more often, and in many cases this is much easier than going to extremes to maximize battery life.
I would just recommend one keep this in mind, a happy battery is a cool and fully charged battery. Use any and all charging sources whenever convenient to get the battery to as high a state of charge as possible.
How long the battery lasts is dependent more on its charging regimen, rather than the quality or perceived quality of the battery. True deep cycle batteries can be a LOT better, but only when good recharging exists. A crappy battery and a top quality battery will both be killed by insufficient recharging/chronic undercharging with the top quality battery perhaps going only a smidge longer before rolling over and giving up.
Worry about top quality battery acquiring when you can recharge them properly. YOu will not really have that until you get some more solar on your roof, or be able to plug into the grid somewhat regularly, but you definitely should utilize the alternator. Alternator charging is far from perfect, and the efficacy will vary hugely depending on the vehicle and its voltage regulator, but it can accomplish a lot with a depleted battery and good thickness copper between alternator and depleted battery.
A battery discharged to 50% might be able to be recharge to 80% in under an hour with a high amperage charging source, but 80 to 100% cannot be accomplished in less than 3.5 hours, and that is at ideal voltages. Vehicles usually only allows ideal voltages briefly after startup. The voltage the vehicle allows will vary widely amongst different vehicle platforms.
Johnct51, lets not scare her by telling the OP that they need to precisely calculate an electrical budget, and to return the battery bought. The loads can be estimated and the battery can be made to work for a period of time. The OP is not looking to set up ideal right off the bat and does not need to be overwhelmed with your ideal approach.
The 12v thermoelectric cooler has got to go though, or only used as a regular cooler and plugged in only when driving. 100 watt of solar could only power that round the clock if the sun never set and there were no other loads.
