Back to OP. Go to GULC if you really want to be an attorney. I agree this sort of seems like you're mistakenly chasing law school for an interest in politics, but I'll leave that alone and assume you want a career as a lawyer (there is little correlation between working in policy/government and going to law school). Taking on $40k debt for significantly improved employment prospects is well worth it. And it's entirely possible (don't know your familial situation, so I could be way wrong here) your parents will see the value of the degree after you make the decision and show them the difference in employment prospects between the two and decide to pay for the difference anyway. It's actually a bit weird that they would quibble over this difference in cost, but again, not familiar with your family's outlook/viewpoint.
It might help them better understand the value of this difference if you show them https://www.lstreports.com/schools/gulc/
and explain how GULC's placement is objectively better in what the legal profession typically considers good employment outcomes (Big law firms & federal clerkships for judges). If you're unfamiliar with these metrics and why they are important, research more first and then explain it to them. They aren't the only good outcomes from law school, they're just the easiest to quantify as good outcomes. Some government jobs are great (you'll see a heavy amount of these at schools like GULC and GW due to their location), but there is nothing in a 509 report to differentiate a less than desirable state government position and doing Honors at the SEC. The same goes for the business category. It certainly could be F500 work, or it could be a barista at Starbucks. Nothing in the reports spells this out.
You're already in a better position than many of your future classmates because you won't be saddled with excessive debt. At that point, it's only prudent to give yourself the best chance of landing the career you eventually want, which GULC definitely gives you a leg up in. Good luck!