Here's how life works. Business exists to create value for the owner. It is up to the employee to provide value to the business, the business does not exist to give you an income. The money you are paid is a by-product of the value you bring to the business.
Businesses have needs, and often, work schedules vary. In retail there are peak hours and 'dead' hours. Businesses need some flexibility in their scheduling.
This is where part-time employment comes in. The more flexible you are, the more potential value you bring to the company. That said, many employers expect you to be flexible and are not going to pay you extra for it. You can be replaced. Your other job and your bills are not the business's concern.
That's the harsh reality. There are a lot of part time jobs out there. It's up to you to make it work. If the business values you enough, they will be willing to work around a first job, which is your first concern.
I had my career job, which came first. For a time, early in my career, I needed extra income so I took a second job delivering pizza. At the time, the shop opened an hour after my normal end time and it was usually no overlap. But there were times during the year where I either had the opportunity to work overtime, or no choice in the matter, at my career job, and if I did, I would be about an hour late to the shop. I made it clear to the shop that my career came first, and anyway, it was foolish to turn down OT that paid me four times what the shop was paying me. As I was one of the top drivers they had and one of the most reliable (turnover was high, it was mostly college kids and I was in my late 20s and stable), they were more than happy to accept my terms.
That is what I mean by bringing something of value to the employer so that they will be more flexible.