For now I would help her with it but be working on individual skills with putting on her clothes. Can she button her buttons? Zip her zips? Get her feet into her trousers? Some children need to be taught these things as individual skills! Teaching a skill in a way that you can make into a song or a game is good, kids like that kind of thing.
Routine is also good. It's ok to play around a bit to find a routine that works for you. You don't have to regiment every minute of the day but a general, we get dressed at this time, we have breakfast at this time, we go for a walk at this time, we have quiet time at this time, will help her "see" the daily schedule and her brain can start self-regulating to the schedule.
Accompanying you in the store is a skill. I find with my ADHD kid that having specific instructions really helps. You need to create a habit that works so you can get through daily life. So, going through the shops, that might be, you hold mum's hand. You need some rules for holding mum's hand. What are the boundaries (think these through beforehand). Do you hold mum's hand in the bathroom? Well, no, not while you are going potty. That would be too silly! Do you hold mum's hand crossing the street? Yes. Do you hold mum's hand while she's pushing the grocery cart? No, how will she push the cart with just one hand? While she pushes the cart, you will hold the cart with one hand. Your other hand can point at things you want to talk about.
Then you create opportunities to practice: go to the store to get one thing. If you do well with following the instructions, you get a tiny reward (a tiny candy, for example). If you aren't able to follow the instructions, then you don't get the reward, but we'll try again tomorrow. This trip has to be short, create a situation where she can win! Don't give in to the desire to get two things or five things. One thing. Next time, increase the difficulty a little bit, this time we'll get two things. And so on. Instead of punishments, you are using rewards. You are creating the conditions for success. You are showing her that you have an expectation she will follow instructions, and that she is capable of meeting your expectations. Over time it becomes a habit.
Sketch out the skill in your mind. What does it look like in practice? If the store is too difficult, .e.g you have to go on the bus and she won't hold your hand there, make it easier. Walk to the corner and back with her holding your hand. Tiny candy if she succeeds. If she doesn't, no matter, we'll try again tomorrow. Calm, cheerful, not bitter or blaming. Keep building it up till it's where you need it to be. Don't make skill-building an overbearing thing that takes up all her time, she will burn out and feel like her day is all work, work, work. One new skill at a time. Be aware some skills she may not be able to build yet. If she can't button her own buttons or isn't strong enough to pull her own trousers all the way up, creating a goal that she will dress herself may be unrealistic.