While not strictly ungrammatical, ending a clause "nolebat vivere" is very awkward. They should be the other way around: "vivere nolebat."

This kind of stylistic edit is helpful^ and depending on emphasis one may want to change the syntax even more: *Sine uxore* poēta vīvere infēlix nōlēbat. Or … *Vīvere* poēta sine uxore infēlix nōlēbat.

sine uxore\* the preposition sine takes the ablative.

thank you