Definitely camping and for the
AAA you need to reserve early or use Rhonda who is a mod here to book for you and she can look out for AAA discounts, but you need to give here you AAA membership number. As others have mentioned especially for kids FW is great and if you can plan for a little longer stay so you can spend some time at the Fort and doing this as a family will make memories that will last a lifetime. Our most memorable memories is our trips to WDW and FW with our sons when they were growing up. When they were teens they really got to bond by pool hopping which was O.K. back then and hitting the various arcades or just hanging out at DTD. You can't put a price on these type of quality family experiences.
We do the AP thing and go for like 40 to 45 days at a time and in that time we will plan to eat out like 10 times, maybe have a midday snack 5 times and we always eat breakfast in the trailer go early to a park, come back for a lite lunch around noon and then eat an early simple dinner around 4 to 5 and then back to a park for 2 to 4 hours in the evening. Of course it's generally just the two of us now unless one or both of our sons/wifes join us and only the single one will stay in the trailer and not every nite since some nites they hit the Boardwalk to all hours and then the single son crashes on the couch at the older son and wifes resort which is usually the WL.
Not sure what you pay or would now pay for plane tickets, but gas costs especially with a POP-UP I would guess would be awash or a little less. With two 4 legged members of the family FW is our only option as it would cost us our first born to board them at home and we are no longer in possession of our 35 YO first born
Larry