Q:"We initially agreed to split the profits 50-50 but after realizing that it was all of my ideas and all of my efforts to market I reduced it to a 70-30 split."
A: Legally you can't do that unilaterally, doing it unilaterally is called breach of contract. So, I presume you got the approval of the coauthor to reduce the coauthor's share from 50 to 30%. Neat, how did you do that without any agreement? Or is that the problem, the coauthor does not agree to a reduction?
Q:"I want to update the book but need to know the best approach-I have several chapters to add. Should I do a second edition with the updated information or rename it so I can just include my name? "
A: You should rename it and probably adopt a series designation. So you would have, by way of example, Series XYZ, Book 1 "The ABC's" and Series XYZ, Book 2 "The DEF's" and Series XYZ, Book 3 "The GHI's", and so on. YOU should trademark the "Series XYZ" with you as the registrant. You should have your copyright attorney register the later two books at the US Copyright Office with you as author alone. The first book should be, if not already, registered by your copyright attorney at the US Copyright Office in both names.
If the reason for any of this is unclear, you should discuss that with your copyright attorney.
I am not your lawyer and you are not my client. Free advice here is without recourse and any reliance thereupon is at your sole risk. This is done without compensation as a free public service. I am licensed in IL, MO, TX and I am a Reg. Pat. Atty. so advice in any other jurisdiction is strictly general advice and should be confirmed with an attorney licensed in that jurisdiction.
What's in a name??? In this case, it does not matter the title of the book. The original creators, you AND your co-author, retain copyright rights in the work. Making a second edition without permission would be problematic. You need an attorney and permission of your original co-author.
Changing the name of the work and not including the co-author does nothing regards to the underlying copyright interests in the work. And, if anything, can actually open you up to a more serious cause of action. When you are seen by a court as having dirty hands your credability is tarnished, so don't try and do anything sneaky here. I also agree with Mr. Burdick in that you can't just unilaterally change the agreement.
Right now, you would likely be considered 50/50 unless you can show (not the co-author) that an agreement was otherwise made. You will need a writing to prove this.
I suggest you discuss the entire matter over with a lawyer in private and see if a best course of action can be reached. Most of us here, including myself, offer a free phone consult.
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What a mess. Here is the good news. Because there is no written agreement, both you and your co-author share in ownership of the copyright of the original book. That means that either you or your co-author are permitted to license or republish the original book, or issue a new addition with updated chapters. Here is the bad new: your co-author will be able to share in the proceeds from your new edition of the book, and you will be obligated to account to him for his share of the proceeds. Depending on the nature of your new chapters, there may be a way to treat them as a separate new work, that you would combine with the pre-existing work and, if so, you might be able to claim 100% of the proceeds attributable to the new chapters (but it is often difficult if not impossible to determine with accuracy the percent of proceeds attributable only to the new chapters.
The other bad news is that you had no right or authority to reduce the split from 50-50 to 70-30. Unless your co-author agreed to this reduction, it is invalid.
This situation could get messy if your new edition generates significant revenues. Thus, the only practical solution here is to work out a written agreement with your co-author that fairly shares the revenues from both the old and any new additions of the book. I bet your co-author disagrees on the value of his contribution to the book and, in any event, you are better off settling with him then expending the money required to fight this out in court.