Pulled up ABRP, looks like you really need a charger in Montgomery. Tesla's website says "coming in 2020" for one in Montgomery but they've also been saying that for one we need in Arkansas. Also has one for Tuscaloosa which would be helpful for this trip if it existed today.
Alternatively, using Plugshare's trip planner, it believes you can drive strait across to Livingston (181 miles) and then up to Birmingham's supercharger (112 miles), for a round trip time of 7 hours and 5 minutes. If you stopped in Montgomery at a destination charger and charged while having a meal, plus L1 charged (110v) at your wife's friends house for an hour or two you would have a little room for unexpected losses. I don't know your exact location or exact destination so this might not work. Also PlugShare believes the car will get all of its 316 miles (I guess I need to update that to 326) which we all know is not that likely on a road trip.
I'd be interested to see what the Y says from its navigation system.