Hello, I am Dr. Elizabeth. I hope that I can help you out today!
Your two dogs are both 12 weeks old?
I thought I would switch over to Q & A as it looks like you are offline now. If I understand correctly, you have two new pups that are 12 weeks of age and you let them out at midnight and again at 5 am.
It is not uncommon for them to need to get out again this early in the am as their bladders are small and their control is still developing. However, I am not a huge morning person and I like my dogs to sleep in later too!
Due to their age, you may need to accommodate their need to get up this early for a little bit. I would gradually try to get out of the early habit as they start to display longer periods of control. If they can already last all day with no accidents, they should be pretty good to make it from midnight to 7 or 8 am!
So, I would feed around 6 pm if possible and then pull water access after 8 pm or so. This should slow down their urine production overnight.
Obviously let them out before bedtime and again at midnight as needed. In the morning, I would ignore them when they wake up early. I know this is difficult and you won't really be getting extra sleep, but just like a baby, sometimes they just need to learn. If they are not in a kennel in your bedroom, sometimes letting them be in the room overnight will help them to sleep better and longer. They sometimes are just needing/wanting to be near their human friend.
Also, in the morning, YOU dictate when they get to go out, be fed etc. When the pups are young, I usually let them out first to relieve themselves (again, not great control initially). But as they get older, I start doing other things first-take a shower, get dressed, eat my breakfast etc. I do this in steps, adding more things to the list. The idea being that there may be other things that get done first and they don't always EXPECT that they go out first. I feed after they go outside and go to the bathroom. They know that the faster they do their business, the faster they will get fed.
So, in a nutshell, I think part of the problem right now is simply that they are young. They will develop more control with time. In addition, they may need to be in the same room with you and this may help. With time, gradually change their schedule and expectations.
I hope that this has helped you and I hope that they learn quickly. Remember, they all learn at different paces. If this has helped, please be sure to click the accept button. If you have additional concerns or questions, please feel free to contact me.