Multiple SSL certificates Apache2 - apache

Question

secure.dynaccount.com (Thawte cert)
http://certlogik.com/sslchecker/secure.dynaccount.com/
api.dynaccount.com (self-signed)
http://certlogik.com/sslchecker/api.dynaccount.com/
httpd.conf
# Thawte certified
<VirtualHost 88.198.55.138:443>
ServerName secure.dynaccount.com
DocumentRoot /var/www/dynaccount.com
SSLEngine on
SSLCertificateKeyFile /var/ini/ssl/secure.dynaccount.com/private.key
SSLCertificateFile /var/ini/ssl/secure.dynaccount.com/public.crt
SSLCertificateChainFile /var/ini/ssl/secure.dynaccount.com/intermediate.crt
SSLVerifyDepth 1
SetEnvIf User-Agent ".*MSIE.*" \
nokeepalive ssl-unclean-shutdown \
downgrade-1.0 force-response-1.0
SSLCipherSuite ALL:!ADH:!EXPORT56:RC4+RSA:+HIGH:+MEDIUM:+LOW:+SSLv2:+EXP
</VirtualHost>
# self-signed
<VirtualHost 88.198.55.154:443>
ServerName api.dynaccount.com
DocumentRoot /var/www/dynaccount.com
SSLEngine on
SSLCertificateKeyFile /var/ini/ssl/api.dynaccount.com/private.key
SSLCertificateFile /var/ini/ssl/api.dynaccount.com/public.crt
SSLVerifyDepth 0
SetEnvIf User-Agent ".*MSIE.*" \
nokeepalive ssl-unclean-shutdown \
downgrade-1.0 force-response-1.0
SSLCipherSuite ALL:!ADH:!EXPORT56:RC4+RSA:+HIGH:+MEDIUM:+LOW:+SSLv2:+EXP
</VirtualHost>

Answer 1

Did you read Apache HTTP docs?
http://httpd.apache.org/docs/2.0/vhosts/name-based.html
Name-based virtual hosting cannot be used with SSL secure servers
because of the nature of the SSL protocol.
You can have one SSL host per IP.
Reason?
SSL connection parameters are set per-vhosts, but must be negotiated before httpd reads host HTTP header.
That give a sense, isn't it?
UPDATE:
Change SSLCACertificateFile to SSLCertificateChainFile and provide correct format of file according to docs or disable client cert verification at all

Answer 2

Your problem here is that you have twice the same ServerName.
In your 2nd VHost, you should have ServerName api.dynaccount.com and no ServerAlias
I'm not sure it's the problem, but give it a try :)
edit:
For the Server could not reliably resolve server name error, you have to define a ServerName in httpd.conf (not in VirtualHost, that will be the default server name)