Ideally, you want the caulk to fill the crack and that is it. You do not want the caulk overfilling the crack. The caulk and the stucco are two different surfaces and painting over this with shiny paint is only going to highlight the problem. I would say going over it with some stucco type texture would be the only real way to fix it, but this could also make it worse if you don't know what you are doing.

The white is pretty. Remove the shutters (found it amusing that you called them “shudders”, read this: Shutters or Shudders). If you read many of these posts, you’ll learn the properly sized and placed shutters (with functioning hardware, or at least to give the impression that they’re functional) are important. But those windows clearly do not work with shutters. I’ll be removing mine when we redo the exterior. Add trim around the windows and paint them a contrasting color. Black works. Is it just this side that bothers you or is the front entry also lacking in your opinion? Post a picture of the entry and one of the house overall to help folks generate ideas.

Horizon Gray would look fantastic with your roof. It is the color of my house. I have Essex Green on the shutters and a gold on the door. I forget the white I used for the trim. I would get a trim kit and trim out your front door. Prune your bushes so that they do not grow past the bottom of the windows.

Adding to my original post - The first pics I included are of the House as it is now. It shows the reddish brownish creamish brick & shows how it looks in different light. The last pic is of the Estate Gray color roof we are having done. I will now post a pic of the cedar color we like for the stain on the replaced posts on the front porch, as well as the Sherwin Williams Mt. Etna color we were thinking of - but it might be too dark...