Since you accepted permanent employment out of state your travel is not considered a temporary work assignment, unless the work is expected to last less than a year. This being the case, your tax home is considered the city or general area where your main place of business or work is located, in your instance Freeport, Tx. There is no regard as to where you maintain your family home.
Your family home is in Mobile, Alabama, but you work in Freeport, Tx., where you stay and eat in restaurants. You return to Alabama every other weekend. You may not deduct any of your travel, meals, or lodging in Texas, because it is consdidered your tax home. Your travel on alternate weekends to your family home in Alabama is not travel for your work or business, so these expenses are also not deductible.
The IRS rules regarding out of town travel are as follows: Travel expenses paid or incurred in connection with a temporary work assignment away from home are deductible. However, travel expenses paid in connection with an indefinite work assignment are not deductible. Any work assignment in excess of one year is considered indefinite.
You may deduct any travel expenses, including meals and lodging, that you incurred while looking for a new job in your present trade or business, though.
I hope this sufficiently answers your questions. Let me know if you still have questions.