My father objected to my going to the summer camp

object to +doing sth/动名词
如果一定要I的话,句子应该改成
My father objected that I was going to the summer camp.
但是用了OBJECTED TO,
后面就必须跟动名词,这里my作为形容我即将去夏令营的一个修饰词,构成了一个动名词结构的短语.my going to summer camp.
所以句子会有my father objected to my going to summer camp!