Collins/Robert gives
ramener
vt Personne,objet to bring back, take back; paix ordre to bring back restore
Je vais te ramener en voiture I’ll drive you back home
ramène du pain / les enfants bring / fetch some bread/the children back
l’hiver ramène les accidents winter brings the return of accidents
remmener
vt to take back / bring back
remmener qn chez lui to take somebody back home
remmener qn à pied to walk somebody back
remmener qn en voiture to drive somebody back
rapporter
vt (apporter) objet, souvenir, réponse to bring back
rapporter qqch à qqn. to bring/take sth back to sb
The problem is the perrenial one of Eng-Fr translation. The English “bring me back something pretty” is completely clear in its meaning, but grammatically short circuited. The thing being brought = something pretty. It’s not literally being brought back though, because that would mean it was originally in place in England. It’s the person who is coming back, and the pretty thing will be brought TO me on their return. The French prefixes r-, re-, ra- are not really fully capable of expressing this idea. “Apporte-moi quelque chose de joli en rentrant” would fully express that idea. However, in my previous post, there are several examples of writers being more lax with these concepts. Furthermore, at GCSE level, I would expect examiners to prefer (r)apporter for objects and (ra)mener / remmener for people, because it’s a kind of rule. I expect that if you asked 10 French people, 4 would use porter, 4 would use mener, and the other 2 would express it equally as succinctly in some other way. BTW I prefer “Bisous” as a sign-off in this kind of familiar message.
P.S. I have a degree in advanced pedantry.