How to use two mail servers in parallel, if possible?

Your application can send mail directly from its application server, provided you take some steps to ensure that your outbound mail doesn't get flagged as spam. This includes setting reverse PTR (DNS) records for the sending server's IP address. Possibly some manipulation of headers and maybe an SPF record...

Another option is to relay your application's mail through Gmail (not worth it) or through another trusted Smart Host.

Also take a look at: Fighting Spam - What can I do as an: Email Administrator, Domain Owner, or User?

If the second server is only outbound for applications, and Google Mail is for inbound and outbound (i.e. normal usage by users), then there is no need to touch the MX record.

Just add the IP of the second server to a SPF Record, which requires access at the DNS level of your domain.

There are several wizards online to assist you in the syntax.

http://www.spfwizard.net/