Since your devices are on separate networks, it's probably due to restrictions placed by your ISP on how you send email.
For example, if your ISP is Comcast (in the US), they will let you send email using one of their SMTP servers -- likely something like smtp.comcast.net. They will not let you send email using an SMTP server from another ISP and usually block any traffic outbound on the standard SMTP port (port 25). This is done to prevent computers within their network from inadvertently becoming spam senders. The side effect is that you have to use their SMTP servers.
If you've verified that this is the case (check with your ISP's site or other support), here are some possible solutions:
- User your ISP's designated SMTP server (google for the name of your ISP plus "outbound email server" or "smtp server" -- or the equivalent in your language of choice)
- Check the documentation or help for the SMTP server you're trying to use for outbound email and see if they offer the ability to connect on a non-standard port. If so, configure Mail.app to use that port instead of port 25.