Op why do you refuse to take any responsibility for what has happened! Let's go through what happened in your own words!
OP- So I went out for the day with 9mo DS. Thinking I'd just be gone a few hours, so could feed him when I got home.
So you chose to go out for the day and had made no back up plan for if you were out longer and DS needed feeding.
OP- So wore a very feeding-unfriendly dress. Covered chin to knee with no openings.
You then chose to wear a dress that wasn't going to be helpful when it came to breastfeeding
OP- As it turned out he wouldn't nap so instead of getting public transport home I walked in an effort to get a pram nap. Didn't work either.
So knowing you were not ideally prepared for breastfeeding your DS you decided that you would walk instead of getting public transport which you knew would add time onto your journey again knowing that your son would probably be hungry and going against your own original plan of only being out for a few hours still knowing your are not in a great position to breastfeed.
OP- asked the lady if she minded if I quickly popped into one of the change rooms to feed the baby as he was probably dehydrated by this time. She said no, it was a health and safety issue. English wasn't her first language so I repeated myself slightly differently to ensure I was understood
You then tried to emotionally blackmail the lady by saying can you feed the baby as he is probably dehydrated to try and make sure you got your own way and then because she refused your request in your own arrogance and belief that because you are breast feeding you can do what ever you want, where ever you want you assumed that because she said no there could be no other reason except that the ladies English was not good enough to understand your request.
OP- As I wasn't keen to remove my dress in Starbucks, I carried on home as quickly as possible in order to get some milk into him (I had offered him water a number of times but he's not very keen on that yet).
Again you chose an unsuitable attire for breastfeeding in and then to top it all off instead of going to an establishment where you could breastfeed without worrying about taking your dress off in front of other people you chose to hurry past them and make out your baby nearly dehydrated because of this shop assistant.
Where does your responsibility for this come in?
Also reading the shops response it is simply paying you lip service to avoid a PR nightmare and probably from having to deal with you again!
Also to make it clear from your misleading title you were not refused breastfeeding in the shop you were simply told you could not use a changing room to do so!