You should post the actual code you are trying to run if you want help with the error message.
But yes, when you += like that on a string, it adds more string to the string.
fkConChildren is not a list, because it is getting the first item of a list, so it is no longer a list. It is the first thing that was in the list. In this case, a string.
Then once you have a list, you can’t use += or + to add a string to a list. You can use list1 + list2 or you can list1.append(anotherString) or list1.extend(anotherList)
Your assigning fkConChildren as the first index of the fkChildren list and not as a list itself containing the first child. To fix it assign it as a list: