How to detect if the mouse is inside the whole form and child controls?

You can hook the main message loop and preprocess/postprocess any (WM_MOUSEMOVE) message what you want.

public class Form1 : Form {
    private MouseMoveMessageFilter mouseMessageFilter;
    protected override void OnLoad(EventArgs e) {
        base.OnLoad( e );

        this.mouseMessageFilter = new MouseMoveMessageFilter();
        this.mouseMessageFilter.TargetForm = this;
        Application.AddMessageFilter(this.mouseMessageFilter);
    }

    protected override void OnClosed(EventArgs e) {
        base.OnClosed(e);
        Application.RemoveMessageFilter(this.mouseMessageFilter);
    }

    private class MouseMoveMessageFilter : IMessageFilter {
        public Form TargetForm { get; set; }

        public bool PreFilterMessage( ref Message m ) {
            int numMsg = m.Msg;
            if ( numMsg == 0x0200 /*WM_MOUSEMOVE*/)
                this.TargetForm.Text = string.Format($"X:{Control.MousePosition.X}, Y:{Control.MousePosition.Y}");

            return false;
        }
    }
}

How about this: In your form's OnLoad, recursively go through all of the child controls (and their children) and hook up the MouseEnter event.

Then whenever the mouse enters any descendant, the event handler will be called. Similarly, you could hook up MouseMove and/or MouseLeave events.

protected override void OnLoad()
{
   HookupMouseEnterEvents(this);
}

private void HookupMouseEnterEvents(Control control)
{
   foreach (Control childControl in control.Controls)
   {
      childControl.MouseEnter += new MouseEventHandler(mouseEnter);

      // Recurse on this child to get all of its descendents.
      HookupMouseEnterEvents(childControl);
   }
}