I've come in late to this situation and it's good to see you've made such progress since your first post. Here's my advice as an experience PTO Treasurer to help avoid some of the challenges you faced with the former treasurer.
Yes, bylaws are essential, but they don't handle all the financial issues. You need to institute some basic (but absolutley essential) financial controls right now, as a condition of existence, so anyone who takes on the new job of treasurer will know what is expected.
1. The bank account must be set up with at least 2, preferably 3 authorized signers.
2. Every check, every check, EVERY check, no matter how small, must be supported by a complete paper trail and have TWO signatures. If the check is to reimburse one of the authorized signers, then the signatures must be from the other two signers (you can't sign a check to yourself).
3. The papertrail should consist of a completely filled-out standard form for each type of transaction, plus a receipt, invoice, or deposit receipt, depending on the transaction. You can get sample forms off the Bonus Tools page of this website.
4. The treasurer must be expected to provide a report EVERY month of the financial activity, plus evidence s/he has reconciled the account. Ideally, the bank statement should be mailed by the bank to someone who does not have check signing authority (but is an officer). The recipient reviews for any odd activity, signs off, and then gives it to the treasurer for reconciliation.
5. Create a budget for the year, and stick to it. If you need to deviate, do so only with a vote of your membership.
6. Have the financial records audited. That doesn't mean you need to hire a CPA. You can have volunteers do it (as long as they don't have check signing authority). You're looking for accuracy, completeness, and appropriateness. A good audit of so-so books will recommend new procedures to ensure better financial controls in the future. Doing an audit shoudlnt' be viewed as trying to uncover fraud. Your new treasurer should insist on an audit before she takes over so she's not responsible for wading thru a mess.
Since you're rebuilding, and breaking in a new treasurer, I strongly suggest you order a copy of the Treasurer's Toolkit from this site. It describes the financial controls above, plus loads more including how to set up a budget for the first time. It also has tips for doing an audit, and a CD with a bunch of tools on it. You might also want to register to use the online Finance Manager system. It's an accounting system sorta like Quicken, but designed specifically for PTO's.
You can tell you new treasurer you all have to abide by these rules because you heard about it from PTOToday. Blaming to big impersonal PTO Today authority takes the heat off you personally so you don't look like the heavy.
One last comment...I noticed you said your treasurer is expected to do the shopping. Can you delegate that kind of work to the committee chairs who need the stuff? I understand your parent involvement is just beginning to grow, so there may not be many people to delegate to. But I would caution you against assuming your treasurer needs to do all the PTO shopping simply because she holds the checkbook. The job of treasurer is pretty time consuming as it is. Shopping for all PTO needs might make it too big a job for one person. We usually reimburse members for authorized PTO purchases after the fact, or cut a check based on an invoice from the vendor.
Good luck with the rebuilding. You're doing the right thing for the right reasons (the kids). Don't give up. If it were easy, someone else would be doing it.