I had a pretty rough childhood. I've always been a bit different (something that I'm now proud of). Not sure if it's spectrum or something else; it doesn't really matter in this context.
I was bullied to the point of physiological symptoms - by everyone except my family. This carried on well into high school (I finally broke free when we moved to a different country). My "friends," at least the closest I had to that idea, all abandoned me in the most demeaning way possible. A teacher picked on me, telling me that I would amount to nothing.
I decided that I would never treat any person that way. Everything changed. I was still (and still am) meak about what is done to me - but I stood up for outcasts. Spreading my time across cliques took effort initially, but it became natural. People started seeing me as a leader, even the popular crowd. The students around me became intolerant towards bullying and ostracization (through avoidance though, not action). I work hard to make people feel special, but it does come off way too too strong right now :).
I'm still broken in many ways, but I am aware of them and work on them. Thanks to the abandonment I experienced, if I feel as though I am being abandoned or betrayed I have an extended panic attack: becoming distrustful and pitiful as it subsides. I'm told I'm attractive, but my mental image is still a 15y/o kid being told "I don't know why anyone would kiss him" by my crush/bully (Stockholm Syndrome much? :)).
It all came down to a choice, spread acceptance, and I've often wondered if explaining that choice would amount to anything. That choice was made more than half my life ago and it is so critical to my being that I couldn't be swayed any other way. If I had chosen to isolate myself, that would have worked perfectly for avoiding those situations - it would have become a reliable and trustworthy solution. Even if I wanted to change that, after being convinced to, it would be habit.
The only real advice I can offer is to teach your children acceptance. They even have to accept the bullies. They have to understand why bullies do what they do. They can be guided to the choice to not repeat what was done to them. I have no idea how to approach an adult with advice: I strongly believe that an adult needs therapy (CBT or somesuch) after a difficult childhood. You just can't let go of nature that has worked for at least a decade based on advice.
I would err against resilience: that is inaction. Becoming the opposite of what tortures you is action.