I know it is hard, I really feel for you, especially when you have a tonne of stuff to do & they seem like they will never give in no matter what you try.
You are however at a very teachable moment in her life. She is figuring out a more grown up style of the 'tantrum'. She has moved on from the toddler variety and is now figuring out if her more sophisticated communication skills can work. The point is here- if you let it be effective this "skill" becomes the manipulation we see in teenagers & adults. She is also learning about something that many adults never learn properly- financial literacy. Shopping can also be a very boring time for children as their parents are busy trying to get stuff done- so the tantrum type behaviour mixes with a bit of attention seeking (for bonus difficulty!)
Luckily these strategies address all 3 issues:
If you can, enlist the help of the people around you to knock this on it's head now. It is important that the people that spend the most time with her are on the same page as you, she sounds like a smart girl- she will figure out who this method works with & doesn't. The frustration & effort will be worth it :)
The main point is consistency. She is old enough now to learn about the theory of conservation. These are the resources we have (i.e money & food) This is what we need (i.e More meat/veges whatever) This is how much potentially you could earn if you look for jobs around the house (the amount is set & can be reviewed on birthdays- or whenever suits your situation, but is negotiable at a time that suits you. Not her)
Get her a money box- ideally it would be good if it is one she can open somehow. Doesn't matter if it is an old container- decorate it together, make it special.
Even 20 or 50p for pocket money is fine.- Whatever you can afford, but do try to give her some & make it the same amount that you will always be able to give each week. A marked calendar might help her understand what day it will happen.
Ask for her help to write the shopping list when you are getting ready (even if you already know what you need- send her to check a few things.)
Play a game where you guess how much things might cost- write this on your list to check. If she begins to ask for things, have a discussion about what are "needs" for the family and what are "wants" and how your family spends on these things.
Get her to write her own list (doesn't matter if she can't 'write' yet- it is for her to read so whatever symbols she uses is ok. Don't focus to much on the writing aspect- you are just writing your lists together- sit together, write beside each other. She can even draw pictures of what she needs/wants.
Maybe you each get one treat in the shopping each week/month and the rest you have to save up for. Use the calendar again to mark when might be a 'free' treat purchasing day. I don't know- whatever suits your budget. If she starts mentioning things she wants that are luxury items talk about how much they might cost & how much she has saved. Does she want to spend ALL of her money on this occasion because then she will have to wait for until she has it again.
Introducing the concept here of delayed gratification (very difficult for this generation but an AMAZING life skill if she can learn it!)
If possible use cash so she can see & understand the transaction.
At the store get her busy looking for things. Checking her list. Checking yours. Finding items for you. Did we get the price right? Did we bring enough money? Can you afford the special thing you wanted? Do you still want to spend your money on it? If she previously opted not to- you say you are really proud of her because it is hard to wait for things you want. Give her a story of when you have done the same. Keep her involved, keep her talking. If the whining starts- try and stay calm & refocus her with a brief & unemotional response "oh remember you have to save for that" or whatever then straight away refocus with a high energy statement "ok! Now where on earth do they keep the BUTTERNUTS! Come on team let's go exploring!" Make that bit fun, make that bit interesting. Her whining is not interesting. You heard it, you addressed it, but it is not possible for x,y,z. We have work to do!
Hopefully you understand what I am getting at here, obviously you need to find your own groove with this. Children want to be heard, they want their concerns taken seriously. So you can acknowledge that she really wants the Dora colouring in book or whatever, but it is not possible because it is not treat day & she doesn't have the money for it. You have explained yourself, now quickly move on to the important stuff. Ignore any other whining, instead continue to refocus with a calm, assertive and firm voice- "_Child's name I really love having your help with the shopping, let's carry on with our job!"
If whining still continues. Now this is the hard bit because any threat you make needs to be carried out- so choose wisely.
Hopefully you have not chosen to shop when she is tired/sick/hungry as if you have she is not in complete control of her behaviour & reasoning with her is an impossible task!)
If you have tried to refocus her 2-3 times, if she continues to whine, stop pushing the trolley & get down at her eye level. Depending on your situation you might say something like " I have told you no. I would like you to listen so we can carry on shopping. If it doesn't stop we will be leaving to shop straight away."
Be silent for a moment so that she understands that you are DEADLY serious. Then smiles and say "come on love let's get shopping!" If the whining continues. Abandon your trolley and leave. It doesn't matter about her pleading, promises, negotiation. That ship has sailed. If leaving the shop doesn't suit- then perhaps it is something like cancelling a play date/trip to the park/whatever next fun thing. The point is whatever you threaten MUST be something that was scheduled that day & MUST carried be out. You should only have to do this once or twice before eventually she figures out that you mean what you say. After that you should only have to get to the threat of it to be effective.
This all sounds harsh- but these are such important life lessons that it doesn't pay to be soft on this.
good luck!