First off, I'm no accountant, but I have successfully completed the 501c3 application process for our PTO, so I think I can offer some insight.
Your PTO should register with the IRS to become a federally-recognized non-profit, tax exempt charitable organization. It is not only the moral thing to do, it's probably the legal thing to do too. Besides being the "right" thing to do, having your 501c3 status exempts your PTO from paying sales tax on purchases (some limitations in your state may apply), and allows your donors to deduct their contributions as charitable donations. It also legitimizes your PTO in the eyes of grantors, big ticket donors, and the community at large.
The one-time IRS filing fee is $500 per organization. It does NOT require an accountant to complete the application, just someone with a nose for numbers and the proper documentation (i.e. past budgets and treasurer's reports). Maybe this is the perfect job for your "difficult" parent. If she is so anxious that the PTO file, she could lead the process! The IRS is very helpful and there are several postings on this site that provide advice for completing the application.
Once you are approved, you must file an annual tax return with the IRS (Form 990). You DO NOT PAY any tax since you are tax exempt, but you must file a completed return if your PTO grosses over $25000 per year. It is not a difficult form, and after the first year, it will be a breeze.
The annual audit is a great idea, whether or not the IRS requires it (I don't recall reading that requirement in any of the IRS paperwork). We had a parent volunteer who is also an auditor review our books for free. His firm gave us a clean review. Technically, it is not an "audit" in the legal sense, but it suffices for our purposes. Why pay an auditor when a parent, or even your own officers could review the files? All you're looking for is that all the checks and balances are in place and the numbers tie out. If you think you need more scrutiny, you may have a bigger problem than anyone wants to admit.
Take a deep breath and look at the situation from the eyes of the other mom. She seems meddling and confrontational. Maybe she's sincere and informed. Don't dismiss her simply because she's not gotten involved for the past 5 years. Maybe she has time now, or maybe she's finally gotten up the nerve to crack through the PTO clique. Be careful dismissing her enthusiasm or you may turn everyone else off. If you only wanted parents to get involved in their first year at your school, you'll be cutting off alot of valuable resources.
I happen to agree with your meddling mom. Maybe her style is abrasive, but I think PTO's could use more people not afraid to challenge the status quo.