Did my neighbor have the right to pull out a gun on my family & me for being on their property?

On Mother's Day...my family (my husband & I & our 3 kids - ages 2, 5, & 10) decided to take a 4 wheeler ride to a small creek near our house. The only way to get there, without driving on a busy highway, was to cross a short distance in the ditch near the highway, which happened to be my neighbor's large front yard. We stayed as close to the edge of their property as possible & drove extremely slow - so as not to leave any marks in their yard. It was not until our way back home that my neighbor came outside, yelling loudly at my husband. My husband stopped the 4 wheeler, got off of it, and walked towards my neighor. He seemed VERY angry - his face bright red - and demanded to know why we were trespassing. My husband explained that he didn't think it would be a problem & that he was trying to be respectful by driving slowly & as close to the highway as possible. My neighbor was not excepting this & became more & more angry & more & more argumentative. Meanwhile, myself & kids are sitting on the 4-wheelers, waiting. Next I see my neighbors wife walking up from the back of her house, with a HANDGUN at her side. CLEARLY at her side - pointing down, nonetheless...but my goodness! Did she really need to carry a handgun to this dispute? To make a long story short, I couldn't hold my tongue - drove my kids home to wait with their Grandma - who was at my house visiting. And walked back to the arguement & said my peice. I thought it was definately wrong to bring a handgun out & near my children was enough to make this momma VERY protective. The neighbors ended up calling the sheriff on US, because they stated we were trespassing & they had a RIGHT to carry a concealed weapon to protect their property. I would like to know if they had a right to do this? We were clearly unarmed & NOT posing any sort of a threat to them - just out for a leisurely, family atv ride, on a nice MOTHER's DAY! Am I wrong?