Welcome to Yorkie Talk.
Most Yorkies and small dogs like to be with their humans whenever possible, so gating your pup in the kitchen at night is likely going to be a long-term battle. An xpen in your bedroom, close to you, would likely be the fastest way to solve your problem, if he is not a candidate for the crate.
The gate does sound like a dangerous situation. If he is a jumper and climber, an xpen might pose a problem too, unless he would settle down being able to see you. You have your hands full. It does get better as they mature.