No offense, but it sounds more like you have difficulty against Ivy as a player, and not just with a certain character. I'll second what Suirad said, and I'd also have to say that Hilde is a bit of a pain (At least, you don't have a definite advantage over her), since she's a generally safe character. Therefore, 236B shouldn't be seeing much use in this match. That said, Hilde lacks decent horizontal mids oustide of her CA moves, and the two that she has are unsafe on block (i.e. 236B punishable). Furthermore, that means most of her close range step killers are high, and Sophie has more than enough TCs to deal with them. Furthermore, your AA is just as fast as Hilde's 6A+K at i12, which should keep her from trying to outspeed you at neutral frames.
You need to stay in Hilde's face for this matchup, so close in with 236236B after an opening (Or perhaps the beginning of the match, occasionally) and try to stick to your faster and/or evasive moves. While countering her standing charges with A+B is fun, but they'll catch on and mix it up if they aren't on auto-pilot charge abuse mode. Also, I need to check out which character is better at SG damage up close (I'm leaning towards Hilde, but I don't know how safe/easy to duck her mainstay SG damagers are). This is a pretty fun matchup, IMHO.
Edit: After a cursory glance at Hilde's SG damage and frame data threads, it appears that almost all of Hilde's SG damagers are unsafe, linear, high, effing slow, or any combination of the four (not that most aren't, but Sophie's got some gems like 4B+K that Hilde doesn't. Also, don't forget her charge moves are somewhat of an exception). Actually taking advantage of these weaknesses is a completely different story, but I'm inclined to believe that a good knowledge of Hilde's SG moves will greatly benefit you. Also, remember to watch out for Hilde's FC charge moves, which are all i18 or i19, and safe on block with the exception of FC C3 BB. Be sure to listen for that distinctive sound, people!