I want to tell a woman to take her dog to the small dog side of the park
Why do you think you need to tell that she needs to move to a different side of the park?
It's my right to tell her to take them out of the big dog side if I want.
Even though it may be the right thing, she may see your actions as being bossed around by a stranger. You should be probably warn her about her dog and how bigger dogs may attack her dog but not demand her to move away to the different side of the park, as she should do that on her own.
Merely a suggestion and I want to make sure that the park is safe for children.
If you think that it will be safer and better for her to move, then you can do so. Just make sure that they will see it as a suggestion, and not a demand from you as they may get angry or retaliate. I hope you have a wonderful time in the park that is free from any conflict.