Don't hit her, that could land you in trouble and put you in a position where you CAN'T protect your kids.

Don't give her another chance, your children only have you to protect them if she is abusive, which means you need to prioritize them above her, because she's an adult with resources that children don't have (if she's abusive, YOU are the only way your children get the protection they need as they legally are very vulnerable if an adult guardian isn't helping them out).

Do you live in the US or a "western" country? Asking because laws and resources for domestic violence can differ depending where you live. Also, are you male?

I think you need to reach out to a lawyer, ASAP, and see what they advise you.

Also, get documentation (photos and bruises and stuff) if your kids are showing injuries. Look up recording laws in your state (one party consent? Two party?) and see if you're able to record your wife's verbal abuse secretly. Keep any evidence you're able to gather in a place she can't get to it. Assume if you leave phones/computers unlocked/without passwords she can see anything on them.

Also reach out to a local domestic violence shelter. Even if your wife hasn't abused you, the local domestic violence agency will have a very targeted list of resources for people in your situation (or kids in their situation) that might be useful for you in your area (including things like therapists for your kids and yourself).

I actually think you might get more targeted advice on how to handle all of this on a divorce-related sub. Mostly because the people here were children of abusive parents, and the way WE get away from our abusers will differ from how a legal adult like YOU will get their children away from an abusive spouse. You have routes you can take that we didn't get because we were minors at the time. As an adult, you will have legal routes to get yourself and the kids out of this situation that the folks here didn't have. But because I didn't go through this from your perspective (spouse of someone abusive) I can't give you the most precise info on how to handle it.

Also, keep in mind...If your wife is an abuser, it may be the second she gets wind of you "turning" on her (even if what you're really doing is protecting yourself and your kids) she'll start throwing false accusations at YOU, or hit you, or harm herself and claim that you hit her. So you need to reach out to lawyers/domestic violence shelters, get some information on how to deal with this, and how to protect yourself from accusations, while retaining your rights to your children.

The exception is if your kids are in immediate physical danger--then call the police ASAP.