Hi Shipahoy,
You could try Oak Mtn State park, which will have the amenities you are looking for
Oak Mountain State Park | Alapark . In addition, Lake Purdy used to be very family friendly:
HOME | Lakepurdy (lakepurdyfishing.com). Both are in the Birmingham Metro area.
Nearby, in Jasper, there is the Sipsey river area where you could also fish for trout as well as panfish, and even some stripers. You can call Brandon and Mary Carole at the little fly shop on the river, I bet they would let you fish on their property behind the shop .
Contacts – Riverside Fly Shop
The Cahaba wildlife refuge is also a great place to fish, (Cahaba River just south of Birmingham), I remember one handicapped fishing platform on the refuge, but it is a little "wild" and away from any real amenities. I have done a lot of bank fishing in all of those areas in the past, I live down in the delta now, however, or I would try to meet up and take yall to some places.
Hope this helps!