Tthe "y" in English and the "y" in Japanese are the same. For exmaple, the word "Yes", I heard a native speaker say it like this: "iiiiiiiiiii -ees. (He said it slowly + put stress on the "y" and that happened), it's not always just the "Y" you think. And Japanese people don't usually squeeze words so of course you will notice the separation between the i and a/o/u sometimes. But there are times when they do squeeze words, so the next time you hear something strange, you don't have to doubt yourself.
So to answer your question "difference between "dayo" and "daiyo" ", my answer is there is no difference, they're the same, the only difference here is you never actually "write" "daiyo" because there is no such a thing in Japanese.
One more thing, the majority of the native speakers of whatever language don't care about what they say nor how it works, please remember that what they say just flows out naturally, they never really think about it. So if you have a question regarding pronunciation, just ask your teacher or your fellow learners because those are people who actually care about pronunciation.