Just remember, you don't have to finish your coloring page in one sitting. If you are looking to produce the best finish possible to your coloring page then don't rush it! Spend multiple sittings, or carve out a couple of hours, but just breathe and take your coloring slow. You aren't working to a deadline and there is no boss to please (other than you!). The only rule you have is to relax, lose yourself in the page and lay down some color.
Embroider around the painted design. Some paints dry soft and flexible. Acrylic paint, however, dries hard. If you are stitching through the painted area, bring the needle through with caution, as making excess holes will show in the paint.