Advice needed

What is your draw per day on the batteries? What do you intend to run on 12 volts?
Charging on solar for 10 hours is only going to get you 1000 watts + - back in the batteries(minus some natural occurring loss)
Most here on the forum will suggest you do not allow the batteries to fall below 50% discharge.

I would check out this blog entry (warning it's long) on people doing what you want to do: boondock on solar. I don't think you are going to get by on one or two batteries nor will a 100 Watt panel be enough:

Handy Bob's

Well reading further down the blog and it's very long, you can get by with a 125 W pannel and a couple batteries if you are very frugal with power use. And if the panel is wired correctly with large enough wire and the controller is placed near the batteries and set at the correct voltage (14.8 V).

100 watts is not a lot, one a bright sunny day you may get 8 amps. :)

Thank you for the quick answers. I don't actually know my daily draw, but in the summer I can often get by without starting a generator for 4 or more days. The Handy Bob link was useful and I will go back and read it again. Yup about 8 amps is what I was expecting and figured it would be on the edge but just didn't know.
I don't use alot of power and really try not to run my generators because the noise bothers other people. I am also investigating an alternate heat source so the power glutton fan on the furnace doesn't run, that too is still up in the air.

How about something like this from Windy Nation? Its not "portable" but can be used as a portable system easy. The panels don't cost much more then 2 battery's and in AZ 200 watts should keep your 2 battery's up nicely. If you are staying in one place for a while its not that big of a deal to set up the panels and it will give you a chance to see how the solar works. After a month using them you will probably end up making a plan to get some solar on the roof of your RV.