Oops

みんな doesn't mean we, but mean "everyone"
Is it correct?

you are right, "みんな" means everyone.

"みんなにあいたくなります。" 　→ "（私は）みんなにあいたくなる"
I want to meet everyone.

Literally translated, "I want to see everyone," but I think it means "I miss everyone" in this situation.

Everyone here might mean your friends living in a place where you used to live, I guess.

Thank you :)

あいたくなります。
＝あい（←動詞「あう」（=meet）の連用形）
+たく（←助動詞「たい」（=want）の連用形）
+なり（←動詞「なる」(=get/become)の連用形）
+ます

In case you can't read マスターさん's explanation, here is the same information in English.

From the verb "au", to meet, we can make the form "aitai", which is often translated "want to meet". Actually, it behaves like an adjective, though, so a better translation might be "desirable to meet."

The expression "become [a certain way]" requires an adverb for the [a certain way] part. So this adjective "aitai" is changed to its adverbial form, "aitaku," when placed before the verb "narimasu (become)".

So literally the sentence means "I am becoming wanting-to-see everyone" (au can also mean "see", in the sense of get together with someone), so Akio-san's "I miss everyone" is the best translation into English.