Please check both sentences and let me know which one is correct.
You can't just order your children to go play while you watch TV.
You can't just order your children to go to play while you watch TV.
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"Go play" is a very common turn of phrase. It's often used as a directive, "Go play, I'm busy." It's also perfectly correct and natural in your first example. That sentence sounds just fine.
"Go to play" is stilted sounding, although it may be technically "correct". The only way I can think of that I would use the "to" in that line is if it also included a location. Even then, I have to mess with tenses to make it sound natural. "She went to play in the park."
I could say, "Go play in the park." I might also say, "Let's go to the park to play." I would never say, "Go to play."