Removing HTTPS binding affects other sites?

My scenario:

• <div mce_keep="true">Multiple HTTP sites (example1.com, example2.com, etc.) on same IP</div>
• <div mce_keep="true">Wildcard *.example.com cert that is used for WebDAV publishing over HTTPS for these same sites (wedav1.example.com, webdav2.example.com, etc.)</div>
• <div mce_keep="true">So each site has one HTTP binding, and one HTTPS (only for publishing)</div>
• <div mce_keep="true">Anonymous authentication for HTTP, Basic enabled for WebDAV over HTTPS</div>

Everything worked fine, until I recently added a new site, which exhibited two problems:

• <div mce_keep="true">WebDAV (XP/Vista clients) get the usual password request, followed by a certificate request</div>
• <div mce_keep="true">I cannot delete the site or remove the HTTPS binding without getting a message like this:</div>

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Site Bindings
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The certificate associated with this binding is also assigned to another site's binding. Deleting this binding will cause the HTTPS binding of the other site to be unusable. Do you still want to continue?
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Yes   No   Cancel  
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I don't know what's wrong with this new site. Apparently the usual setup steps were followed, but now I can't even delete it out of fear of losing the wildcart certificate that is also used by other sites, and I am a bit at loss.

Any advice?

Thanks!