<p>^Not if you want to include all possible definitions of “family,” which is far broader than the typical nuclear family with two parents. It’s not really easier to say it one way or another.</p>
<p>I would interpret “family” without a modifier like in “extended family” to mean the immediate nuclear family, i.e. children plus parent(s)/guardian(s).</p>
<p>Also, I’m not sure how many colleges actually ask whether you’re the first generation to attend college. They may just draw this information from asking parents’ education, which is a required section on the Common App. (If there is actually a question on the CA, ignore this.)</p>