You need to stay on I-10 or below it. Do not even think about going any where north of I-10.
How much time have you allowed? Remember, 1-10 is almost 1000 miles across Texas, so that will take a while. Where in Arizona are you going? I would suggest you make Van Horn your last night in Texas, and the next day drive clear to at least Las Cruces - we usually go to Deming because we're Escapees and there is an Escapees park in Deming.