am I correct?

I got an e-mail today:

"Hina-san mo kittekureru yo, demo muri wa shinai de moshi tsugou ga yokattara mata asobi ni kitte ne!"

I understand that it means Hina is coming too, and does the second part mean something like "if it's okay with you and you can, let's go do something later"?

"Hina-san mo kittekureru yo, demo muri wa shinai de moshi tsugou ga yokattara mata asobi ni kitte ne!"

Something along the line of:
"Hina-san is also coming. You don't have to go out of your way, though, but if it's okay with you, please come visit me again!"

"tsugou ga yokattara" = if it's convenient for you; if the schedule works out for you
"asobi ni kite" = please come visit with me (to have a good time, etc.)

I think throughout the e-mail, "kitte" (te-form of the verb "kiru," to cut) should be replaced with "kite" (te-form of the verb "kuru," to come), though. :)

Ah, thank you! You're right about kite/kitte- I just typed wrong when I was transcribing.

One more question: what does " muri wa shinai de" mean when just used by itself? I've heard it before- like when I was trying to decide whether or not I should leave a party since it was getting late, one of the hosts said something like "muri wa shinai de". I have never heard it used like that before so I didn't know if he was saying "it's not trouble (ie you should stay)" or "don't trouble yourself (ie you should go)"

kind of an important distinction! ^_^;

"muri (wo) suru" means to "push oneself to do something," "do something at excessive trouble/cost," etc. Therefore, "muri (wa) shinaide," or "muri wo shinaide" (which uses the negative te-form of the verb) = Don't go out of your way; don't push yourself; don't take extra trouble to do something.

If someone said that to you when you were trying to decide if you wanted to leave as it was getting late, as that person must have wanted you to stay longer to enjoy more time there, I assume it was "(it would be nice if you could stay longer but) don't stay too long if it's not comfortable for you."

Used in the context of the e-mail, where the person says "muri wa shinaide,moshi tsugou ga yokattara..." he/she is saying that "since Hina is also coming (it would be great if you can come), but you don't have to take the extra trouble to shuffle around your schedule, if the schedule works out, it would be nice if you can come."