Does my Research Card from A1 and A2 allow access into other NARA locations?

Yes, if the card is still valid, it is acceptable at National Archives field office.

Although you didn't ask I just want to add--for full clarity in case other people have questions and find this post later--that presidential libraries maintain their own systems with regard to researchers so you would need to register at any one of them.

If you return to A1 or A2 and your card is expired, please bring it with you. The renewal process is quicker than re-registration and you won't run into troubles with any copy money you may have stored on it.