Well... You could play it cracked? The Tekkit server has to be set to offline mode. I tried it when my TechincLauncher was failing on me. Still was able to go on a cracked server. But I would recommend setting the server limit to 2 people since its only you two so that it would lessen the chance for a hacker to get in. You might need Hamachi since its you two as well. No point port forwarding and everything for a small server.
Hope this helps
[Edit] : I recommend getting minecraft cause if you crack, you can only play with your brother or in a private server. If I'm not wrong the default name for a cracked player is '' Player ''. So mostlikely there can only be one cracked player in a offline server. Idk, never really tested it out.