The children were Mamie and Charley who was my cousin's grandfather! I'm pretty sure Mamie eventually married Emile Strain after his first wife died because Alice's obit says she was foster mother of Mrs. Emile Strain of Abita Springs, LA. The 1900 Census says James was born in Ohio as were his parents and Mamie and Charley were born in Louisiana as were their parents. I'm thinking that maybe Mamie and Charley were the children of a relative. My cousin's mom told her that Charles's father's name was also Charles. Also, if James were the children's father, Alice would have been their step-mother.
If you've found anything else since your original post, I hope you'll share!
Leslie Bedron Blankschen