Can someone point me where in the Reg it has information on if a customer reopens an account we have to give out a Truth In Savings Disclosure?

I do not know of any consumer protection law that recognizes the idea of re-opening an account; Regulation DD does not. A "re-opened" account is a new account for all purposes and they are a wellspring of compliance errors.

Pete's Mom, when your institution re-opens an account, what do you consider the opening date? The original opening date, or the date it was re-opened?

This may be your answer here... Commentary of DD...

Section 230.4 Account disclosures

(a) Delivery of account disclosures

(a)(1) Account opening

1. New accounts. New account disclosures must be provided when:

i. A time account that does not automatically rollover is renewed by a consumer

ii. A consumer changes a term for a renewable time account (see §230.5(b)–5 regarding disclosure alternatives)

iii. An institution transfers funds from an account to open a new account not at the consumer's request, unless the institution previously gave account disclosures and any change-in-term notices for the new account

iv. An institution accepts a deposit from a consumer to an account that the institution had deemed closed for the purpose of treating accrued but uncredited interest as forfeited interest (see §230.7(b)–3)

§230.7(b)–3. Closed accounts. Subject to state or other law, an institution may choose not to pay accrued interest if consumers close an account prior to the date accrued interest is credited, as long as the institution has disclosed that fact.