Hi all not sure if that is the correct place to post this question

I am booking a flight on AA.com
With AA from SAP(Honduras) to MIA with a 2.40h lay over. and then with SWISS to ZRH

What happens if i miss my connection due flight delay, luggage claim and checkin and or immigration.
Would i have to talk to AA or SWISS?
Would the charge me for the new ticket?

We tavel
-with kids
- on swiss and honduran passports
and we are not used to travel