try this

;however, over this past summer, …..

“Having only been on it three times, it remains as the only roller coaster I’ve ever ridden. However, over the past summer, my parents decided to take me, my little sister Brianne, and my cousin Michelle, who is also my age, to Disney World for graduation.”

or use a semi-colon “ridden; however, over…”

but if you do want to keep it the way it is, you do need a comma after but.

Having only been on it three times, it remains the only roller coaster I have ever ridden. However, this past summer, my parents decided to take my sister, my cousin and I to Disney World for my graduation.

Something like that removes all of the needless details and gets right to the point. Hope that helps!

you have too many commas in this sentence. you can rewrite as

“Having only been on it three times, it remains as the only roller coaster I have ever ridden. However, over this past summer, my parents decided to take me, my little sister Brianne, and my cousin Michelle, to Disney World for my graduation.”

however and but are the same, but if you use however, you need to use either semi-colon or period in front of it and a comma after it.

“my parents decided to take my sister, my cousin and I to Disney World for my graduation.”

you dont use “I”, you use “me”. take “my sister, my cousin ” away from the sentence. then you have “my parents decided to take I…” that is wrong