It comes as a surprise to a lot of homeowners that chimneys DO occasionally need to be rebuilt. It's just that rebuilding a chimney typically only needs to be done once every 80 to 100 years, and so it's a relatively rare event. Your chimney definitely needs to be rebuilt, and any bricklayer can do that for you. Also, you might consider having a metal "liner" run inside your rebuilt chimney to extend the life of the chimney brickwork even more.
What you need to do is ask your contractor whether the cracks in the exterior stucco are due to building movement, such as a deteriorating foundation. If so, then repairing those cracks may only be a stop gap measure, and the stucco could continue to crack.
You might consider something called an "elastomeric coating" instead of repairing those cracks. Years ago there was an old children's toy called "Stretch Armstrong" where "Stretch" was made of an elastomeric rubber. No matter how far you stretched "Stretch" out of shape, he would always return to his originals shape. That's the trick behind elastomeric coatings; they stretch across gaps in plaster or stucco, but shrink back to their original position if the crack closes up again. If you have an older home without a solid foundation, using an elastomeric coating to keep the rain out of your walls and cover those cracks may make more sense than trying unsuccessfully to fix them. You need to have a contractor take a look at your situation to determine why the cracks are occuring and whether they can be fixed permanently. If not, then it may be a wiser choice to allow the cracks to open and close, but to keep the rain out of the walls by using an elastomeric coating.
PS: If you do opt for an elastomeric coating, be careful about picking a colour you're going to be happy with for an awful long time. That's because elastomeric coatings are applied much thicker than latex paints, and so they last for very much longer than latex paints. In fact, some companies even market elastomeric coatings as "permanent exterior paint". You can't simply paint over an elastomeric coating with a latex paint because latex paints simply can't stretch and shrink as far as elastomeric coatings can, and so the paint will break loose from the elastomeric coating. Any paint store should sell elastomeric coatings, or you could find them using Google, too.