Hi Howard,

For applying Sherwin Williams Gallery, sanding between coats can enhance adhesion, especially if you're adding a third coat. While it's not strictly necessary to sand between every coat, lightly sanding (using 220-320 grit) after the first coat and then again before applying the third can help ensure a smooth finish and better bonding.

Regarding painting the jambs and casings, lightly sanding the existing Emerald semigloss acrylic latex with 320 grit is a good approach. This will help the new Gallery paint adhere better. Make sure to clean the surfaces afterward to remove any dust before applying the new coat.

For detailed guidance, you might find these resources helpful:

• Sherwin Williams Technical Data
• Painting Tips from Sherwin Williams

Feel free to reach out if to me on my Houzz account if you need professional help.