I agree with @ren_grantz interpretation. おとなを感じさせる is using the causative form of the verb 感じる, and since the (implied) topic of Papa’s thoughts is Satoshi and not himself, the thing that gives the feel of an adult has to be Satoshi and not Papa.
Hmmm… I’m not very confident, but my interpretation was that Satoshi was saying he’d let go of Papa’s hand if a friend came. If he was asking Papa to let go I would kind of expect him to use “離して” or something along those lines instead. I might be wrong though.
Maybe it helps to think that こころ also means mind, his mental side. こころの成長, thus, is his mental growth, his maturity in a psychological sense. As @ren_grantz pointed out, this seems to be referring to the fact that Satoshi is already showing interest in girls.






