The "correct" way (the way professional database designers do this) to do this would be to create another table called "list_info" which would hold all of the children's names individually. Here's what the database would look like:
user:
userid int primary_key auto_increment
username
password should use a hash or encryption scheme, such as md5
location
list_info:
list_info_id int primary_key auto_increment
parent_id int
child_name
Using this design, every user would have a userid (which you should almost always use, so that every entry has a unique ID# attached to it), and the userid in the user table would be linked to the parent_id in the list_info table. When you want to add a child, you enter another record in the list_info table, putting their name in child_name and their parent's id# in parent_id.
If you're insistant on using just one table, though, you can read the list_info value into a PHP variable, and then append what you want onto the variable (using the .= operator) and update the mysql record. But I would be very reluctant to do that, as it makes the database less usable.
Of course, you can choose your own names for the tables and fields, the design is what's important.
