I figured out how to do this. For those who may be wondering how to do this, I'll spell out what I did. And if there is a better way, please respond.
I added style="display:none" to those elements on the tag_a.ascx page (Link tab) that I did not want to show (this is according to another post in this forum) and made other modifications to fit our needs. And to prevent the General and Style Builder tabs from showing, I added the highlighted code to the tag.frame.aspx as follows:
foreach(XmlElement xe in doc.DocumentElement.SelectNodes("add"))
{
string tab=xe.GetAttribute("tab");
if(IsTagPattern(tagName,xe.GetAttribute("pattern")))
{
bool isactive=(index==0&&(tabName==null||tabName==""))||(string.Compare(tab,tabName,true)==0);
if(isactive)
{
tabcontrol=xe.GetAttribute("control");
tabtext=xe.GetAttribute("text");
}
%>
<some html code>
<%
index++;
/*Break if this is an anchor tag to prevent the General and Style Builder tabs being added to the Insert Hyperlink dialog*/
if (tagName == "A")
break;
}
}