<font face="Verdana, Arial, Helvetica, sans-serif" size="2">It is my understanding that adults may not fly in exit rows if they are traveling with children under 15, even if kids are seated in non-exit rows, for obvious reasons.</font>
Not exactly. You're referring to sec. 121.585 of the FARs, which states the requirements/restrictions for those in exit rows. It only says those caring for "small children" may not sit in exit rows.
From the FARs - reasons for not allowing a person to sit in the exit row:
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(7) The person has:
(i) A condition or responsibilities, such as caring for small children, that might prevent the person from performing one or more of the applicable functions listed in paragraph (d) of this section; ... </font>