Has anyone ever forced an abusive adult child (30) with 2 kids (3&6) to move out? What is the best way to accomplish this? Cautions to take?

There is only one way to get unwanted residents out of your house and that is with a legal eviction. It doesn't matter what the relationship of the resident is. Go to your local Housing court and find out the rules for evicting a tenant, because they qualify as a tenant and follow them.

If he gets violent, then call the police and try to get a restraining order.

Basically there are two options: evict formally through the courts according to the laws of your state (some consider everyone tenants, others also have a provision for 'lodgers' that can get them out sooner), or call the police about provable violence and get a restraining order. I'm guessing that you are going to have to take the first route.
The cautions to take with eviction are all about retaliation, so lock away your valuables and stay home as much as you can, and maybe even move another (sympathetic) relative in for a while.
You can't change locks or throw things out onto the street.
Of course sometimes the eviction process leads to events that do call for police intervention and an RO.
You can tell us the state, or Google 'tenant law your state' or go to your local court house and ask.

What do you mean by "abusive"? Please be specific. If they are physically abusive, are they armed? That is an important point. Are they mentally/emotionally abusive? Are they financially abusive? Does the abuse extend from the use of drug or alcohol substances?

The answer to these questions will give you some direction into which avenue you take. Should they be armed, and the abuse is severe enough, then get your butt out of there! Forget restaining orders (which aren't especially helpful) and orders of protection (which don't mean a whole lot more). Give no indication that you're leaving. Just go. You may pursue all of the legal actions you want later. But for right now protect yourself. I hope this helps, and good luck.