I did a PhD in mathematics, though in a country where it is treated as a full time research job with a fairly livable wage and other benefits, so I didn't have a job on the side. What I'm about to say may not apply 1-1 to your situation.
I couldn't imagine working a job while doing my PhD. For me, it took a lot of time and effort to produce some original and worthwhile results, and I cannot imagine having done so while working another job on the side. It takes (for me at least) quite some mental acuity and freshness to produce any worthwhile results, and I don't think the job will help with that. What's more is that it can take a while to produce anything worth it, and the longer it takes, the more emotionally draining it is. And the worse you feel, the worse you perform. It's a vicious cycle, and anything reinforcing that negative feedback loop is something to avoid like the plague. A lot of PhD students end up with mental health problems because of this. I think you should not do this.
This is just my personal experience, but from talking to my peers, and reading about the experiences of others (also in more US-like systems), I gather that mine is not atypical. I remember reading a lot of stuff like the above before I started, and thinking that I was immune to depression or something, it never dissuaded me. I wish it did. I hope for your sake you find something that'll convince you not to do a PhD while working a job.
I always thought "divorced emerald mine inheritor" was quite apt.