It would help to let your attorney know what you told the police because the police are specifically trained. Everything you tell them they're going to be written down.
They're going to be asking you questions with the intent to elicit responses that incriminate you. They're going to go through all their field sobriety tests.
You're going to want to tell your attorney what you told the police because that is some of the information that's going to be used in trying to convict you.
Tell them why the police pulled you over, how fast you were going, whether you got in an accident, and whose fault it was.

Be honest with your lawyer about how many drinks you had. There's no reason to lie to your attorney.
They're not looking to tell the prosecutor; they're just looking to figure out whether there was an accurate blood-alcohol level or whether you need to hire an expert.
If it's a breath test, they're going to need to decide whether or not they want to check to see if the machine has been appropriately calibrated and whether there are any issues with it. Tell the lawyer exactly what happened.
Do You Advise Pre-Trial Counseling For Your DUI Clients?
If you think you have an alcohol problem, you probably should do voluntary counseling to help yourself so you don't get yourself in this situation again.
If I think it makes sense, I'll try to use it with the prosecutors. If you don't believe that you have an alcohol problem, I don't think you need to enroll in any alcohol program immediately.
The prosecutors don't care about it, and it can even have the opposite effect because they're going to say you have an alcohol problem and need additional penalties.