I’ve provided a working example that follows your second approach. Updating the component’s state is the preferred way to show/hide children.

Given you have this container:

<div id="container">
</div>

you can either use modern Javascript (ES6, first example) or classic JavaScript (ES5, second example) to implement the component logic:

Show/hide components using ES6

Try this demo live on JSFiddle

class Child extends React.Component {
  render() {
    return (<div>I'm the child</div>);
  }
}

class ShowHide extends React.Component {
  constructor() {
    super();
    this.state = {
      childVisible: false
    }
  }

  render() {
    return (
      <div>
        <div onClick={() => this.onClick()}>
          Parent - click me to show/hide my child
        </div>
        {
          this.state.childVisible
            ? <Child />
            : null
        }
      </div>
    )
  }

  onClick() {
    this.setState(prevState => ({ childVisible: !prevState.childVisible }));
  }
};

React.render(<ShowHide />, document.getElementById('container'));

Show/hide components using ES5

Try this demo live on JSFiddle

var Child = React.createClass({
  render: function() {
    return (<div>I'm the child</div>);
  }
});

var ShowHide = React.createClass({
  getInitialState: function () {
    return { childVisible: false };
  },

  render: function() {
    return (
      <div>
        <div onClick={this.onClick}>
          Parent - click me to show/hide my child
        </div>
        {
          this.state.childVisible
            ? <Child />
            : null
        }
      </div>
    )
  },

  onClick: function() {
    this.setState({childVisible: !this.state.childVisible});
  }
});

React.render(<ShowHide />, document.body);