It's very clearly spelt out in the UN Convention
The security guard and store manager have direct/implied instructions to stop any big dog (guide dog or not) before this incident.
She was trying to educate them by arguing that it was a guide dog and probably had already spelled out the whole document.
It is totally 鸡同鸭讲 (chicken and duck talk). Nobody will budge.
If her point is to get in and "see" the dress, just leaves the dog with someone and goes into the shop for a quick "look".
If her point is to get the dog into the shop, then she was making a mess out of it.
If her point is to educate the shop, forgets it.
If her point is to be more famous, she got it.
If she wants to sue the shop, goes for it.
There are only 6 guide dogs currently in Singapore.
Please do not expect a quick change of mindsets just because of the document (legal or not).