Cattlemen's Texas Longhorn Registry ctlr.org
As PZ said, this has to be re-built to modern web standards and the content updated (notice the copyright date). The code errors on your domain name home page speak for themselves.
[Invalid] Markup Validation of http://www.ctlr.org/ - W3C Markup Validator
You say you have a database but you don't mention the software you're using so I must assume it's desktop software like Excel or Access which is not compatible with a web site.
My impression of this is that you've been "getting by" for so many years with outdated methods that you pretend it's working well & think you can keep doing business as usual. I don't think that's realistic however.
These days, an online presence means putting your best foot forward & giving people what they want.
a) A quality presentation that looks great & compels people to use your services over the other guys.
b) A functional site that provides a good user experience without clunky workarounds.
c) A site that performs well on all web devices -- mobile, tablet & desktops.
To that extent, your site falls way short of expectations.
This is a do over. No question about it. If WordPress was recommended to you by an experienced developer, you might want to take them up on it.
Nancy