My computer launches the new tekkit fine, but my wife has this exact problem so we can't play together. Been trying to figure it out all day.
Are you all running 32 bit or 64 bit windows? Java 6 or Java 7?
You might be able to do something with a light-detector from redpower. I haven't tested it but in theory it gets darker when it rains so...
EDIT: ninja'd by minutes
There's a rain collector in Forestry mod that can do it i think, but I think that's only Technic.
Where are you located? I do run a small personal server (rarely more than me and one other), but if you're far away the ping won't be great, I'm not on any kind of super connection.