^^This is a good way to start the poem and catch the reader's thought! It will make the reader wonder about the lines that are about to be read. Maybe a coma at the end of sentence will be better.
That loving compassion of the mother for her child
That dwells in each one of us
^^A mother's love for her child is precious. She will get angry, she will scold but her love never diminishes. We all have that sentiments and compassion; we have to learn how to extend that compassion to others as well even if they are strangers or not your child.
I also feel that line will read better if you remove the word "that" for it looses the flow. Perhaps something like this:
"The loving compassion of a mother for her child
That/which dwells in each one of us.
So it can embrace the whole of humankind
Bringing happiness to all
^^A true sentence. When we learn to embrace the whole humankind, peace will indeed reign. A coma after the second line will be good here.
The joy of living
Intensely rooted in the life-force of the cosmos
^^Here too I feel the flow is abrupt, maybe the breaking up the lines will be good. For instance:
"The joy of living
in the life force of the cosmos.
Overall, a lovely poem that holds an universal message, which needs to be enforced now more then ever! That is when peace will envelope the world.
I also hope you didn't mind me pointing out the little details/changes in the poem. I felt this was such a good read and wanted to enhance it more.