Yes, you’re reading it correctly: the PRODIGAL Father. Sure, the son was prodigal in his wasting of his inheritance on vanity, but check out this definition of prodigal:
adjective: marked by rash extravagance
And so it is with the Father’s extravagant love that could be judged by some as rash. His loving kindness is poured out on us, no matter how low we go. Isn’t it wonderful? Forgiveness abounds.