좋은 하루

오늘은 나의 조카딸이랑 그녀의 동생과 함께 해양 공원에(aquatic parc marineland in Antibes) 갔어요.

with Niece and she's sister?
나의 조카딸이랑 그녀의 동생과 함께
or
with my sister and she's daughter?
나의 여동생과 그녀의 딸과 함께

조카와 돌고래들을 보았어요

내 조카딸은 스물두살 이에요. 내가 보기에 그녀는 돌고래들과 좋은 시간을 보냈어요.

This sentence means. 'My niece is twenty two years old. My point of view, she spent good time with a dolphins.' right?

My point of view(내가 보기에) she (그녀는) spent(보냈어요) good(좋은) time(시간을) with a dolphins(돌고래들과)

오늘은 나의 조카딸와 동생과 함께 앙티브에 있는 아쿠아리움(aquarium in Antibes)에 갔어요.

In dictionary, "niece" stands for 조카딸, which is féminin because of the attachment of "딸(fille)" but we don't use the word like this--we just say "조카," which is neutral so is also appropriate to designate a "nephew."

For "aquatic parc marineland," we usually say 아쿠아리움, the transliteration of "aquarium" and if it is in Antibes, you might add "앙티브에 있는" or "앙티브의" before that.

조카와 돌고래를 보았어요.

Korean isn't so much strict with the plural form of nouns unlike English or Française. Sometimes I see a translator strictly attaching the plural ending "들" to every noun and make the entire sentence look awkward in consequence.

내 조카는 22개월이에요. 돌고래 공연을 무척 좋아했어요.

I guess your translating program did a quite bad one with this ;) Probably the machine translated "the show" as (in Korean) "the, seemed" and then messed the whole meaning of the sentence.

"The show with the dolphins" would be simply translated as "돌고래 공연(the dolphin show)." Or literally, it would be "돌고래가 나오는 공연(the show which stars the dolphins)."