Yes it does sound like part of it is a control issue. I agree to be sure that her diet is rich in fruits, vegetables, and grains which are high in fiber. Also be sure that she has enough liquids. Prune juice and prunes will help. You can mix the prune juice with another juice such as pear to make it more palatable to her. Continue with the Miralax. Mirilax works by drawing fluids into the bowel and thus softening it. Cut out dairy, including ice cream and cheese. They can cause constipation. Live organism yogurt may help.
I would tell her that you are now going to rely on her to poop when she needs to. Explain to her about the health hazards of not pooping. Sympathize with her when she does try to poop and isn't able or it is painful. Tell her that the more she doesn't poop the more painful it'll become. Tell her that you know she can work this out for herself and that you will take her to the toilet after meals because that is when most people poop. But that if she doesn't want to poop that is OK. You'll trust her to poop when she's ready.
It will take awhile for her to trust that you really aren't going to bug her. And it will take awhile for her body to learn how to have frequent softer stools. Have some toys and books next to the toilet, potty chair so that she can go in and sit down to play. Be light hearted with her. Make sitting on the toilet/potty chair a fun thing to do. Pooping is to just be a by product.
This did probably start out because she was constipated and it was painful. Now, after you've understandably paid a lot of attention to her not pooping, it has probably become a power issue. She also senses your anxiety which increases her anxiety, causing her body to tense up. Several different things are going on.
Try to relax.. Let her know that her body will figure it out. Encourage her to relax. Focus on regular trips to the bathroom that are fun without focusing on her having to poop.
It's a two pronged approach. Diet and relaxing, letting her have the control.