A user control should be an isolated whole, a container.
You need to use events.
Think about how you would make a regular Button control populate some text in a regular TextBox control?
The TextBox doesn't know about the button and the button doesn't know about your textbox. They are separate controls.
What you do is subscribe to the button's click event, and then tell the textbox control to change it's text.
Similarly to that, your user control needs to provide and Event that you can trigger whenever a button click or some other action happens.
That is all that the control should do, provide an event and trigger it.
It is then appropriate for you to subscribe to that event from the form where you house your user control and in that event handler change the other control's property as needed.
The following is a brief example of how and Event works. Find more info here
This should be inside your user control
//A delegate that describe's your event's signature
public delegate void ChangedEventHandler(object sender, EventArgs e);
//The actual Event declaration
public event ChangedEventHandler Changed;
//When appropriate, trigger the event from the user control
if (Changed != null) {
Changed(this, e);
}