Hi there!
I also use a kennel for my puppy. When I used to wake up in the middle of the night I would set my alarm to get up ONE time in the night (that is plenty IMO) and we would get up, put him in the bathroom and potty and back to bed. No play, drink, kibble, nothing. It was strictly to potty. Also, at Petsmart the trainer there said that if you give them time to "wake up" so to speak, then they think it's morning and time to play. So just wake up, hurry up, and get him out, potty, and back in. Hope this helps!
P.S. Mine only had to do that for a couple months, and now he goes all through the night, but first thing in the morning is him pottying.
I hope this helps! Good luck