This is something that I have struggled with for years, since giving my life to Christ. It is not just a problem for those with three small children! It is making the choice to meet with your maker and communicate with him INSTEAD of watching tv, reading a book, playing on the computer, etc. The Holy Spirit is speaking to me, telling me that it is a perfect time to go and read my Bible and pray to God. I cannot begin to tell you the thousands of times that I have not listened to that still, small voice--and I have done other things.
Setting aside a time that works for you is key. The Bible has many verses about meeting with God in the morning, which is ideally the best time--since this is the beginning of your day. However, if that time is not going to be something you can commit to--find a different time!!
I have found that right before bed can be a good time--but again, by the time I find myself crawling into my bed--I just want to sleep!
For a mother of three, the afternoon or evening might be best.
I have quiet moments in the afternoon while my oldest is at kindergarten, and the other two are napping. It is a perfect time to pause and rest in the Lord.
The evening, after the children go to bed--is hit or miss. The kids do not always get to bed when they should, and sometimes the baby is up again for a short time before going back to bed at 9 or 10.
So, by replying to this question--I have discovered for MYSELF--the afternoon would be the best time for me.
This prompts me to make a commitment to do just that and see how it works out.
Thankfully, our God is a forgiving God--patient and understanding--and always ready to give us yet another chance!