If I am a shaliach for lighting someone’s menorah, do I make שעשה ניסים twice (once when lighting for him and once for myself)? Does the same halacha apply to שהחיינו? There is no way to light both without a hafsek in between.
It depends if there are other people that you will include in your bracha at home. If you will be motzei others, then you will make the other brachos because of them. However if you are only lighting for yourself then you would only say להדליק and not שעשה נסים nor שהחיינו .
See M:B 671-45 regarding שהחיינו that if he lit in shul and he has other to be motzei at home that he can then say שהחיינו, even though he already said it, but if he isn’t being motzei others he shouldn’t. He doesn’t say anything regarding שעשה נסים. However see Zichron Shalom pg. 655 (from R’ Yosef Shub Shlit”a), that he brings Ohr Zarua 325, Shiuriei Tahara- Maareches 8-3, Pri Chadash 676-3, and Birkas Habayis 54-4, that all say regarding an instance where someone didn’t think he would be able to light chanukah candles the first night, and therefore he made שעשה נסים and שהחיינו upon seeing someone else’s candles. Later that night he got the opportunity to light his own candles, that he doesn’t say those two brachos if he is’t being motzei someone else. This would be similar to your case, where the person already made the other two brachos, and now he is lighting at home.
All this I heard from R’ Y. Shub shlit”a regarding your question.