April is absolutely prime time for severe weather, but that usually only takes half a day to blow through. My advice, therefore, is to go ride and leave yourself an extra day or two to hole up in bad weather. And check the weather forecast before you head out in the morning; the forecasters will always highlight bad weather ahead of time (usually they'll predict the end of the world 12-24 hours before it actually arrives).
April is prime weather for riding, except for when it's not. You can expect light breezes, comfortable cycling, trees budding out and azaleas to start blooming the end of the month.
Direction? There's 100 miles of 6% grades on the north end of the Trace. I'd plan on riding north, myself, and plan two days for the Tennessee portion. You'll get used to the longer daily rides before you cross the Tennessee River (in Alabama, naturally), and be ready for the hills. The day you're feeling really strong will probably be the day bad weather's coming in the afternoon, as storm fronts are preceded by S winds shifting to SW and W before the squall line arrives. Then you'll have 24 hours of strong N winds.
I don't know about the southern portion of the Trace, but services are sparse on the north end. Florence and Muscle Shoals are about 10 miles off the Trace, and that's the end of nearby services until you get to Nashville. You (or your wife) will be using some web searching talents to find restaurants and B&Bs near the Trace in Tennessee; it's often 30 miles to a small town.