I'm not sure Karoline would necessarily be in an either-or position, TBH. Sarah's was a position of intimate friendship that went horribly south w/o Witty Jack to keep his wife in line. Unless Karoline's taking over as Anne's lady-in-waiting (unlikely), the Sarah>Abigail>Anne triangle would still continue. As to a rival, it's not impossible. Compared with Karoline (indeed, compared with the much older Electress Sophia), Anne's as dull as ditchwater with regards to vivacity, intelligence and beauty (she's been described as dowdy in one bio I've read - and that was before she acquired the nickname of Brandy Nan for her like of a tipple once too regularly - although, TBF, I think it might've been (or at least started out) for medicinal purposes). Karoline, OTOH, is probably the center of the new court (as the princess of Wales), the future (as it were), while Anne is the past (so there's going to be rivalry on those grounds. Not least because it's the struggle between a mother and a wife over the prince of Wales). So, IMHO, it's not unlikely that when Sarah and her husband fall out of favour with Anne, they do what they did OTL and cosy up to the heir to the throne. In fact, considering that Marlborough was in the duke of Gloucester's household OTL, it's not unthinkable that Sarah serves the duchess of Cumberland (Anne) while Jack is in the household of Gloucester (maybe even their son, Jack Jnr, survives and is good friends with Gloucester (or your TTL future king), that whichever way the cat jumps, the Churchills have an in at court.