Normally, in a TextBox cell, if you have a blinking edit cursor in the middle of the text, the arrow keys will move to the edge of text before moving to the next cell. But if the whole text is selected, it just moves to the next cell. There is no property setting that will change this behavior and still let all the text be selected.
To get the cell control to use the arrow keys, try handling the CurrentCellControlKeyMessage event.
private void gridControl1_CurrentCellControlKeyMessage(object sender, GridCurrentCellControlKeyMessageEventArgs e)
{
Keys keyCode = (Keys)((int)e.Msg.WParam) & Keys.KeyCode;
if(keyCode == Keys.Left || keyCode == Keys.Right)
{
e.CallBaseProcessKeyMessage = false;
e.CallProcessKeyPreview = false;
}
}