Hey @kariforuniajin !
In this sentence, 行く is conjugated using たい to create 行きたい ‘want to go’ and くなる is added to create 行きたくなる ‘I ended up wanting to go to the bathroom’. When the grammar point になる・くなる is attached to a verb conjugated using たい it will follow the conjugation rule of a い-adjective since たい is conjugated in the same way as い-adjectives.
We hope this clears it up!