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It was your child who tore my book to shreds.
Literal
I [of-の] book [object-を] to-bits tore-apart [nominalizer-の-は] your child is.
The [clause]+のは+[noun]だ pattern is a cleft construction — 'the one who [clause] is [noun],' used to focus on who/what did the action. Here it identifies the culprit. ばらばら is a 擬態語 for 'in pieces, scattered,' and with 引き裂く it means 'tore apart into bits.' 引き裂く is a strong compound verb: 引く ('pull') + 裂く ('rip').