There is nothing obviously wrong with the situation that you have described. The best thing that you can do now is to Google IRS Form 1023 and read through all of the questions. You should pay special attention to Part V, which has questions like "Have you adopted a conflict of interest policy consistent with the sample conflict of interest policy
in Appendix A to the instructions?" Work with a lawyer in Texas who has submitted a great many tax-exempt entities to the National Office of the IRS for favorable determination letters.
There is nothing specifically wrong with requiring preapproval of a number of officers or trustees for any expenditure for a nonprofit organization. Frankly, it sounds like your organizational documents are little unusual. You really need to have a tax lawyer help you prepare the correct articles of formation, and bylaws (many times called constitutions by nonprofits). You did not state what your nonprofit organization does, but depending upon its activities, the IRS may have a higher level of scrutiny.
I hope this helps!
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I agree with the other posts by my colleagues. I would add that the IRS does not look at bank records initially so unless this information is volunteered it should not come up unless your governing documents state what you have recounted. However, practically speaking as well as best practices usually allows the Treasurer to be a signatory on accounts. I am not sure how this would affect grants on its face. Watch out for "Founders Syndrome" whereby a Founder of an organization perceives the organization as his or hers.