How to transfer users between different domains?

Question

Active Directory

Good afternoon!
Situation: There is a firm with one domain on 2003 Windows Server. There is a separate (already now) organization in the company (in the form of OU (Let's call it "Horns and Hooves")). It so happened that all users of the Horns and Hooves organization were brought into this container.
Now it is planned to allocate a separate (including geographically) server for the needs of the organization. It is planned to raise 2008 R2 on it and start your own separate domain (with all services such as DNS and DHCP). All machines are already working in a new place, and in the domain they are authorized on that distant server.
I was faced with the question of minimizing employee downtime and my efforts to move.
Task: Migrate AD user credentials and, if possible, computer accounts, to the new domain.
What was tried: Raised a 2008 domain on a virtual machine and tried to export (successfully) all users and import (failure, cursed. Error codes will be given later) to the new domain using the csved and ldifde utilities.
Perhaps there are some utilities for transferring users between AD (with saving passwords or not?)
Add. the question is - if you leave the domain name the same - will it be necessary to restart the machines in the new domain?
Thank you very much for the answers, I will clarify your questions as they are asked :)

Answer 1

Of the standard - ADMT. Available for download from the Microsoft website.