getting a puppy to sleep later

Question
I actually have two questions.  First of all, I have a nine week old puppy that has been living at our apt. for the past two weeks.  We have her sleeping in our sons room in a crate.  I slept in the room the first three nights and had my son sleep in a different room so that he would not be interrupted and would have a good night sleep and be well rested for school the next day.  The puppy cried a few times during the first two nights for about 10 minutes and would than go back to sleep.  She woke up for good about 6:30 (which is Ok).  The third night, she slept straight through until 6:30.  I moved my son back into his room and we had a good routine going for about 5 nights.  Suddenly, two nights ago, she woke up crying at 4:00.  My son tried to ingnore her but she started barking like crazy so he took her out to our gated kitchen and played with her for about an hour until she went back to sleep under our bed.  I let her do that so that we could get some sleep.  Last night, I moved back into his room and at 4:00 she started barking again.  I can ignore crying but I can't ignore barking since we live in an apt. building.  What can I do now that she has started barking when she wakes up?

My other question is, I've put this gate up in the kitchen so I can keep her confined and away from my rugs while we are home.  The gate has been up for two days now and if she is left alone in the kitchen, she barks most of the time if she knows we are home.  We spend a lot of time playing in the kitchen with her until she gets tired in the hope that she will sleep and we leave lots of toys to keep her busy but it doesn't seem to make any difference.  We ignore her barking for quite awhile so she won't think that barking will bring us back to the kitchen but it is driving us crazy!  When we leave the house and we leave her in the kitchen, she does seem to stop barking.  At least when we come home, it's quiet.  She really doesn't like to be left in her crate either and has the same reaction.

I hope you can help me out.  She is an adorable Labradoodle but she is driving us nuts!

Answer
Usually when they wake up in the middle of the night, they need to go out to relieve themselves.  Taking her out might help get her to go back to sleep again.  Usually they don't consistently sleep through the night until after 2 months old.  

As for the second problem, you must spend more time with her.  Dogs are pack animals and expect to be with their family.  I actually shuffled things around making room for a computer desk in this room with the hard surfaced floor so the puppies and I could be here together.  You will either have to spend more time in the kitchen with her, or let her into the carpeted rooms.  She is getting big enough to reduce the number of accidents.  By learning to recognize when she needs to go out and promptly taking her out, you can greatly reduce them.  It requires you to be very attentive to her.  Actually leaving her in another room where you can't see her is going to cause problems housebreaking her.  

There will still be accidents.  You might look at buying a ''Spot Buster''.  Even people that don't have puppies find them useful.