Sometimes children having a hard time getting to sleep or calming down can be the most challenging aspect of parenting (at least for me!).
One thing we have done with my son is turn relaxation into a game.
We start out in the living room. If it is night time, all the lights are off and he would sit on my lap in the lazy boy. I would use a very soft voice and say, "Can you hear what I hear?" and then he would say what he could hear. Fortunately for us, we live in a very noisy area. He would name the obvious things like a train or airplane or cars passing. I would then name something softer like the refrigerator. I would wait several minutes before asking him what else he could hear.
When we ran out of things to listen for in the living room, we would move to his bedroom. I would sit on the floor and he would lie in bed. I would say what I heard and wait for his reply.
This activity would take between 20-25 minutes and usually happened after we read books and our son would get out of bed to complain of being scared, hungry, thirsty, etc.
I have never tried this when our son was mad or noncompliant, however I assume it may work as a de-escalation technique for a child.