Isn't this saying "I shouldn't" twice?
No, not quite. The direct translation is more "I should refrain from drinking that", which would normally be expressed in English as "I should not drink that".
I see where I went wrong now - there would need to be a "ddim" after "Ddylwn i" to make it "I should not." Thank you!
All mean 'I should not drink' There is no reason for the mutation of ddylwn... in the original sentence, as there is no fe/mi marker or anything else to cause it.