I am not sure if the 「やっと」 would mean 'at last' or relate to any specific Japanese dialect. Here is sentence including the words in question.
だから わしが特{とく}別{べつ}におねがいして やっと おまえたちも入{にゅう}場{じょう}することもゆるされたんだ。
おとなしうせにゃいかんぜ。
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Sign up to join this communityI am not sure if the 「やっと」 would mean 'at last' or relate to any specific Japanese dialect. Here is sentence including the words in question.
だから わしが特{とく}別{べつ}におねがいして やっと おまえたちも入{にゅう}場{じょう}することもゆるされたんだ。
おとなしうせにゃいかんぜ。
やっと is a standard Japanese word. It means a desire has finally come after difficulties or long time.
The second sentence is おとなしう/せにゃ/いかん/ぜ。. This sounds a little bit old, yet I think this is not a dialect but euphonic changes.
おとなしう → おとなしく "behave yourself"
せにゃ → せねば "if not be"
いかん → いけない "must not"
ぜ → ぜ
Literally, it means "If you do not behave yourself, it is bad."
The whole translation: "Because of it, I asked them exceptionally, and finally, you are allowed to enter too. You must behave yourself."