To Wake or Not to Wake?

I became a Christian when I was a freshman in college. The next year I got involved in a Christian fellowship group and learned about something called a "daily quiet time" or DQT. (Since we had an acronym for everything!) I then got into the habit of spending time each day reading my Bible and praying. It was a good thing.
I continued with this practice through college and into my married life, until I had kids. Then it pretty much went out the window. Oh, I tried, but I was tired and overwhelmed with baby stuff and just couldn't seem to bring myself to manage fitting DQTs into my life, too. So for years, my "quiet times" were probably monthly, or semi-monthly at best.

God is so gracious, though. I love that although I wasn't making time for Him, He never let up on His love for me or His desire for me to know Him. Over time, I came to understand His love for me is not dependent upon my performance, or my keeping of spiritual disciplines. Nothing I ever do will increase or decrease His love for me. He loves us because He chooses to love. With that understanding, my gulity feelings for not having quiet times faded and my desire to have those quiet times grew!
While the desire was there, I still couldn't imagine how I could make it work. Then I was at a TimeOut for Women! conference and one of the speakers, Nancy Leigh DeMoss, gave us a "30-Day Challenge." Nancy had been talking about God's desire for intimacy with us and closed with a challenge for us to spend some time alone and quiet with Him each day, for the next 30 days. She gave some practical suggestions on how we could do it (like getting up earlier, but I don't want to get up earlier!) and that was the push I needed. I accepted the challenge and began a new leg on my journey with God.

It has been about a year and a half now that I've been getting up (most days) at 6:00 and spending time praying, studying God's Word, and enjoying His love for me. Though I realize that window of time from 6:00 to 6:40 is no more holy than any other time of the day, God is no less present to me the rest of the day, and He doesn't love me any more now than He did two years ago when my "quiet times" were nearly non-existent, I have come to cherish and even crave these times with Him.
That brings me to today and the question pressing on my mind. It used to be that I got up at 6:00 so I could have these peaceful moments with God before I woke the kids at 6:40 to get ready for school. One day Elizabeth got up at 6:00, too, to have extra time in the morning to play a computer game or work on an art project. That wasn't a big deal. She was pretty quiet.
Then Joshua started asking me to wake him up at 6:00 so he could play computer games, too. And my quiet time started getting a little noisier. Now Matthew has become a regular part of the 6:00 bunch and I'm thinking I need to take the word "quiet" out of the time I spend with God in the morning. (As well as the concept of "alone.")
This morning I "pulled Elizabeth out of bed" like she asked me to, to make sure she would get up. Then I half-heartedly wakened Joshua and told him he could get up if he wanted, though I was hoping he'd say he wanted to stay in bed until 6:40. Matthew didn't need any help. He just got up. (This does leave me wondering why I have to work so hard to get him out of bed at the times when I really want him up...)
I came downstairs, settled into my chair and began to look at Psalm 34:7. The angel of the Lord encamps around those who fear him, and he delivers them. Then Joshua settled down next to me to play a computer game, and I asked him if he would please take it into the other room. He agreed reluctantly, but at least he agreed. Soon a conversation began between Joshua and Elizabeth, but I tried to tune them out and just imagine the angel of the Lord encamping around me.
Just then Matthew stood before me with a bowl full of oatmeal. Turning on his charm, he said, "Mommy, would you be nice enough to make this oatmeal for me?" I wanted to say/yell very sarcastically, "No! I'm trying to meet with God here! Would you just leave me alone?!?!?!" I knew that wouldn't be a good response, so I got up and made his oatmeal. I noticed, though, that I had become quite grumpy in the opening minutes of my "quiet time." "Grumpy" is not the behavioral disposition I'm hoping to obtain each morning, and I started getting teary as I considered what was going on inside of me. So I put Matthew's oatmeal on the table for him and went up to Elizabeth's room to journal and pray and try to sort things out with God, while echos of the kids' voices resounded from below.
Part of me thinks the kids shouldn't come downstairs before 6:40. They don't need more computer time. They could use the extra sleep. I could use the peace and quiet.
Then I wonder, "Am I just being selfish?" Selfishness and I have a long history with each other and I'm trying to break things off with it, so I question my own motives a lot. I'm wondering, is it selfish for me to want the kids to leave me alone for this 40 minute window of time? Am I just spiritualizing my own selfishness?
I want to delight the heart of God by the things I do and say and by the person I'm becoming. I believe that starts by me spending this time with Him each day. It delights my heart to be in His presence this way. But something isn't working now and I'm not sure what to do. Anyone have some words of wisdom and experience to share with me???