Why doesn’t the “share” option appear on my lists neither under “my list” section in remainders? Please help me I really need to share with my family some lists😔

You're not tapping on the right thing. The three dots have nothing to do with it. You need to tap on the sharing icon. If you don't see that, it may be because you haven't enabled Reminders in iCloud. See here for more information:

Share lists and collaborate in Reminders on iPhone - Apple Support

Because that's not how you share a list. You need to tap on the sharing button:

You can share a list and collaborate with people who use iCloud. People who accept the invitation can add and edit items, mark items as completed, and all the collaborators can see everyone’s changes. Everyone you collaborate with must be signed in with their Apple ID and have Reminders turned on in iCloud settings.

1. While viewing a list, tap .
2. To change the access and permissions, tap the share options below Collaboration. You can set either of the following:

• • Allow access to only people you invite.
  • Allow others to invite.

1. Choose how to send your invitation (for example, using Messages or Mail).
2. If you send the invitation in Messages, you get activity updates in the Messages conversation when someone makes changes in the shared note. Tap the updates to go to the shared note.

Glad you got it sorted out! I had to read the help document a couple of times before I was sure how it all worked.