This is almost certainly meant to be a representation of spoken Japanese. The person is speaking and describing this kind of person. First the speaker offers "笑いかけるような," but deciding that isn't enough, simply interjects a そんな to be kind of like, "you know", in English. So it's like, you know, that kind of pattern where like.. you're describing something but, like, in the middle it's punctuated with these.. you know.. verbal cues that indicate thought about how to expound upon the subject.
笑いかけるような is modifying 子. So is 人を疑うということを知らないような, obviously. The そんな I guess is technically also modifying 子; essentially the three are aiming to be the same thing, both in meaning and therefore in grammatical role. What kind of 子? そんな子. そんな子ってどんな子？人を疑うということを知らないような子。笑いかけるような子。