How can I prevent the Enter key from moving to the next cell when the user is actively editing the cell and presses Enter

Override the method ProcessKeyPreview in your DataGrid.

protected override bool ProcessKeyPreview(ref System.Windows.Forms.Message m)
{
	Keys keyCode = (Keys)(int)m.WParam & Keys.KeyCode;
	if((m.Msg == WM_KEYDOWN || m.Msg == WM_KEYUP)
		&& keyCode == Keys.Enter )
		return false;
	return true;
}