whose 在本质上相当于物主代词 one's,很显然 one's 前面是可以连用介词的(如果语境需要的话),这样的用法太常见了。如:
She lives with her mom and dad. 她和爸爸妈妈一起住。
Dan covered his face with his hands. 丹用双手捂住脸。
Too much tea is bad for your digestion. 喝太多的茶会妨碍消化。
同理,whose 引导定语从句时前面也完全可以连用介词(如果语境需要的话)。如:
I'm not in the least bit interested in whose fault it is. 对于是谁的错,我一点儿也不感兴趣。
There is a case with whose problem we will deal. 这个事件是包含需要我们去解决的问题。
The family at whose house we stayed were friends of my father’s. 我们曾住过的那家的主人是我父亲的朋友。
I apologized to the woman on whose toe I stepped while dancing. 我向在跳舞的时候踩到她脚趾的那位女士道歉。
The surgeon on whose skill her life depended came to this country from Sweden. 他的技术救了她的生命的那位外科医生从瑞典到本国来了。