Let me preface my question by letting you know that I did all the things I was supposed to. I wrote a book. I proofread many times and edited it. I walked away for a year and came back to it. I let about fifteen other people proof and edit it. I walked away for another month and then came back. I tweaked and tinkered. I made the story tight. It was perfect. (Or so I thought.) I sent three chapters off to an LDS publisher.
To my utter horror, I realized later that the whole first chapter is unnecessary and distracting. I should just delete it. But, it is one of the three chapters I sent. I tried so hard to keep that chapter in, but I now know that it would be a much better book if chapter two were really chapter one.
Here's the question,
How unprofessional is it if a publisher requests your full manuscript and when it arrives, one of the original chapters you submitted is different or deleted from your full manuscript? Did I make that clear? What would happen if I sent in a chapter that is different than the one they read? I think I already know the answer to this, but thought I would ask because I'm sure I'm not the first person to contemplate this and I won't be the last.
First, wait and see if you get a request for a full. If you don't, then simply send the revised version to other publishers. If your first version was close but not quite on the mark, you may get a response asking for you to rewrite and submit again. If that happens, send the new version, no explanations needed.
If you do get a request for a full then you have to make a decision.
There is a type of writer that is very difficult to work with. They are constantly doing major rewrites to their manuscript, even after acceptance. They'll often make changes that I haven't asked for and sometimes I don't notice until it's almost too late—throwing the schedule way off. If these changes made the book better, that's one thing. But more often than not, their rewrites are not better, just different. Sometimes worse.
When I have a writer like that, or think a new author is going to be a writer like that, it makes me hesitate. Sometimes their book is worth the pain in the neck. Sometimes it's not. You do not want me to think you're that type of writer.
If they ask for a full based on the original version, it means the old beginning wasn't as bad as you think (nothing to be utterly horrified about). If you really feel the new beginning is significantly better, include a cover letter with your full that briefly explains (in 1 short paragraph or less) how the beginning different and why it's stronger/better.