A website can only have one SSL certificate at a time.
If you had uploaded the self signed certificate first, and then got a GoGetSSL certificate and replaced the existing self signed certificate with it, then the self signed certificate is gone.
The Delete Certificate button is indeed broken, but that doesn’t really matter. Because you can just replace the old certificate with a new one whenever you want. And removing a bad certificate won’t fix your website, it will just give you a slightly different SSL error.
Where do you see this danger page?
It sounds more like a caching problem to me, or maybe something is actually interfering with your connection. If you have a GoGetSSL certificate installed, then you should not get a danger page at all.