Do the math.
Let's say you stay at your current job, and work 12 hours a week, every week, for a year. There are roughly 50 working weeks in a year.
So your maximum pay, before taxes, at the part time position is:
12 hours a week * $17 an hour * 50 weeks in a year = $10,200 a year.
Now let's say you take the full time position. I'm assuming 40 hours a week, again for 50 weeks out of the year.
So your pay, before taxes, at the new job would be:
40 hours a week * 50 weeks in a year * $13 an hour = $26,000 a year.
That's more than two and half times what you make now.
But let's say this place only considers 30 hours a week to be full time (a lot of places are beginning to do this.)
30 hours a week * 50 weeks in a year * $13 an hour = $19,500
Almost twice what you make right now.
But wait, there's more.
You say the new job would also provide health and dental coverage. That's easily worth a couple thousand dollars a year that you aren't paying.
AND you get vacation pay, meaning you still get paid (about $100/day) even if you take the day off, as compared to your current job where you don't get paid if you don't work.
So, I dunno. It seems like a no-brainer to me. Do the same work, get paid more. Substantially more.