Re: teaching writing an invitation letter in informal style
You need the "how are you?" to be its own sentence.
Your change to "I want to share good news with you" is better, but "some good news" is better yet.
There is no reason the whole family can't be excited - leave that alone.
"So" is a very logical connector. You should leave that alone too.
The order of "on October 4 at 7 pm" was also fine. Don't change your students words when they are not wrong.
There is nothing wrong with "I hope to see you soon."
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.