We don't want to have to show panic.

We're not going to show panic and that's exactly what I did.

1.  don't want to have to do 这个表达，have to 不可删掉，因为它表达两层意思：“不想”+“非要做某事”。删掉后，第二层意思就没有了。英语中，这样的表达很多：

However, he didn't want to have to pay for his wife, as well.
然而，他不想非要为他妻子的花费付钱。
I don't want to have to tell my kids that the years speed up as you get older.
因为我不要将来也对我的孩子说，年纪越大，时间就过得越快。

2.  be going to 和 will 表将来，除了语体的差别以外，还可以表示“主观打算”，本句含有“不打算；不想”之意。强调主观意图。