こんにちは。 接する here means like “deal with” or “treat”. I find the sentence very charming, with 大人に『は』and 『やら』なければ. Kind of like ... “When it comes to grownups, small people always have to put up with them and try to treat them with tolerance and generosity.” Have fun!

In this context, 接するmeans "communicate" or "treat" .

「子どもは大人にはいつも広い心で接してやらなければならないのだ。」 In this sentence, who does this action "接する” for whom? Children have to do for adults. I mean the doer of the verb 接する is 子供 because it has は. Moreover, 「大人」 has 「には」, which stands for to/for (This is the dative case). この文脈を合わないかもしれません。 Therefore you are confused. If adults must do that task, say 大人はいつも広い心で子どもに接してやらなければならないのだ。