Mother's love [I think you are referring to YOUR mother's love, so you would use the possessive 's for Mother]

My childrens' winter vacation started this week. [again, use possessive 's because it the the vacation of your children]
Last weekend I went to the city where my parents used to live. [I am assuming your parents don't live there anymore]

My mother told me , I could go, and leave my children with her at home.
So I went alone. My mom missed my children and wanted to spend more time with them.
I think she is extremely busy now that she is taking care of my children. Thanks to her help, I have more free time.
I know that she did that (take care of them) for me.
She really wants me to take a break from raising my kids to help me keep my stress down.
How can I make her happy?
The more I raise my kids, the more I feel my mother's love.
I know that I can't love her more than she loves me.
Thank the Lord that I'm my mother's daughter!