Mentioning original submission in re-submission?

If it's to the same place you'd want to, otherwise they might think you're sending the same story again. Say how much their feedback helped you and that you revised based on their comments.

The question to ask is; did you get a personalised rejection or a rewrite request?

They're not the same thing. Feedback is always very welcome but I wouldn't resubmit something unless the editor had specifically asked me to make some changes and send it back in.

Of course you mention it to the same publisher (g). I had a similar experience before my first novel was accepted. I submitted hundreds of submissions to agents/publishers, always getting a standard form letter, like "Thanks, but no thanks. Don't get depressed. Good work, just not for us." No real feedback, no constructive comments.

Then after 14 months of submitting, I got a detailed response from a publisher that stated what they liked, and what they did not, with specific suggestions. The letter was a whole page. I'm sure if they had not seen some promise they wouldn't have dedicated the time, but the point is, it was tremendously useful feedback that I could understand and I rewrote the novel (took 4 months). I resubmitted to half a dozen publishers and received two acceptances, all because that one publisher took the time to give useful valuable feedback. Its one of the many reasons I submit to them first for all my new novels. People like that deserve some loyalty.

Do they accept resubmission? Did they ask for a rewrite?

Then again, what do you have to lose? They may just reject you again.