RSA had a 'direct' book of business which they sold to the AA. RSA still underwrite the policy and handle the claims, but the AA issue the renewals, handle any customer queries and collect the premiums.
I presume that your relative had a policy held 'directly' with RSA (ie not purchased through a broker) and now RSA are writing to tell her that her policy admin will be done by the AA, there is no change to the T&C's, cover remains the same, expect some correspondence from AA, that kind of thing.
Shoddy of them not to respond to two separate letters requesting an explanation. If she/you write again, address the letter to the CEO and I'd say you'll get a reply.