Sounds like something is missing, i.e. are you 15, 25, 35, or 75? Are you stealth camping or staying in Marriotts? Are you or your mom concern about being in shape? Are you going solo or with others?
I agree that bike touring in the countryside is less dangerous than in a city but remember that Moms are supposed
to be worried.
Maybe have your mom read some journals of people riding through Texas over on CrazyGuy. It sounds like this might be your first tour. If so, do a route that is already known and researched, i.e. the Southern Tier in Texas, so you can say "Look Ma, I might meet some other riders who are on this exact route which has been researched by a great organization and has had thousands of people ride it." You gotta make Momma happy cause if she ain't happy, nobody be happy so go on a organized route first. Once you get this first tour done, she might be a tad less stressed and you can go on other trips with less guilt for worring your Mom. It took my Mom 8 years of annual tours (including a 4 month, 9,000 mile tour) before she mostly, but not entirely, became comfortable with me touring.
Do a weekend tour first close to home so she can get more comfortable with the idea of you touring. You could also get a Spot tracking device so she knows where you are at all times. Consider riding with others. Worse case, do a weekend drive of your route so she can see it for herself.
I really don't understand the "just doing it" part of your statement. Does she have a concern about this or you?
I know this may not help much but just consider this practice for when you get married and you have to convince your spouse every year that you will be OK
Out of curiosity, where is your route going?