I'm using a monitoring software that sends out email to my ISP's mail server (SMTP Server). But sometimes, the ISP's mail server goes down, or takes too long to respond, I would like to find out if there's a Windows software/proxy that can forward the email to another mail server, e.g. Gmail, Yahoo mail, etc.
If you want to do things 'right', a local Mail Transfer Agent (MTA) such as Exim or Postfix will handle this easily. This sort of routing decision is what MTAs are designed to do.
If you have in-house expertise around web handling and no local SMTP expertise, then in the interests of using tooling that your folks are likely already familiar with, you can deploy nginx as an SMTP proxy and configure multiple backends.