How do I know if I am a competitive applicant for a top/second-tier grad school?
There is one thing that comes across clearly to me based only upon what you've written. I believe you are a very hard worker and you are willing to take risks. These two characteristics are very attractive to many people.

I think you need to concentrate on writing a succinct (but complete) résumé that showcases all of your accomplishments and evidence of positive character traits. To answer your main question, I already have a clear sense that you are definitely competitive. Your GPAs have shown an increase over time and you have a unique history. This means you also have a unique perspective on life.

If you spend money on anything, you'd probably get the most bang for your buck if you had a professional write your résumé. Then, you could make edits to that to suit your own personality. Get that done quickly and then start applying to lots of schools. Don't spend any more time worrying about whether or not you're competitive. You are. Stop worrying about making mistakes. This isn't life or death, it's simply grad school. Just make sure that spending money on grad school will actually amortize in a reasonable amount of time. I think it will definitely do so for you based on the avenue you are interested in pursuing.