update database between 3 forms?

Fire an event from form-3, something like DataUpdated. Handle this in form-1 and act accordingly.

[Edit]
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In response to your comment, here's some sample code that shows what I mean (you should be able to adapt this pattern into your project):

class Form1 : Form
{
    Form3 form3 = new Form3(); // form3 instance

    void LoadInternal()
    {
        form3.DataUpdated += Form3_DataUpdated;
    }

    void Form3_DataUpdated(object sender, EventArgs e)
    {
        ModifyData();
    }

    void ModifyData()
    {
        Form2 login = new Form2();
        if (login.ShowLogin())
        {
            ModifyInternal();
        }
    }

    private void ModifyInternal()
    {
        // update the grid
    }

}

class Form2 : Form
{
    internal bool ShowLogin()
    {
        // prompt for auth details
        return true;
    }
}

class Form3 : Form
{
    public event EventHandler DataUpdated;

    private void FireDataUpdated()
    {
        var temp = this.DataUpdated;

        if (temp != null)
        {
            temp(this, EventArgs.Empty);
        }
    }

    public void Foo()
    {
        // some code that updates details

        FireDataUpdated();
    }
}

[Edit 2]
~~~~~~~~
In response to your comment, it's an event that you define on your Form3 class. And it's handled from Form1. This is a very popular approach that's used for inter-form communication in Winforms.

[Edit 3]
~~~~~~~~
In response to your comment, var is just a shortcut for implicitly typed local variables. In my code example, that will resolve to EventHandler at compile-time. Seeing that you are rather new to C#, that may sound odd to you. But the reason I did that is for thread safety. Since delegates are immutable, and since the backing store for an event is a delegate, you may run into a race condition where an event handler is unhooked in one thread even as another thread is firing those events. To avoid this situation, a local variable is used to create a copy. For now just ignore that and use the code directly.