Insecurity is caused by wanting permanence, is it not? We feel fear and insecurity when we are anxious about the root anchors of our life being unstable.
In truth, one who understands anicca knows nothing is permanent. At a very deep level we must see that resting on inherently unstable emotional platforms and expecting stability is folly.
There is no easy cure for this. We must at the very least learn to dissociate our identity and sense of self from worldly factors such as a job, a relationship, a degree, a house, a bank balance etc. This can be done through any of the several forms of vipassana.
UltimatelyIn the end, we must lose all sense of self by seeing its illusory nature.
What helps me is to take time out to go on a retreat and try to solve a sticky problem in my life through better understanding of anicca, anatta and dukkha.
ULTIMATELY, there can be no perfect relationship where no one hurts the other, or misunderstands. If there were such perfection possible, then that would replace the dhamma, and everyone would aspire for the perfect parent or partner. These imperfections in relationships are our teachers, helping us realize the futility of chasing happiness in relatives and family. Every pleasure carries with it a tragedy - pleasure and pain cannot be separated. One can only go beyond both.
Update: (This was part of my original answer but because of a bug in the mobile client of StackExchange it didn't get posted.)
Here is a short meditation mindfulness exercise by Thich Nhat Hanh to deal with anxiety in the immediate moment.
Sit comfortably. Close your eyes if possible. Gently focus your attention on your breathing. Don’t worry about deepening or controlling it in any way…just notice.
As your breathe in, say to yourself “I am breathing in.”
As you breathe out, say to yourself “I am breathing out.”
Continue for one minute.
The effects are cumulative, so the more often you do it, the faster your overall level of calm increases.
“Breathing in, I calm body and mind. Breathing out, I smile. Dwelling in the present moment I know this is the only moment.” – Thich Nhat Hanh