If it were me, I would want to be contacted by my husband who cheated, so I don't recommend not trying to contact her. Yes, she may need to blow off some steam, but she needs to hear you say that you are sorry and that you won't do it again. She probably won't be able to believe you at first, as she's too hurt and angry, but she needs to hear you say it. Later, she may come to believe you, depending on how things go.

My husband cheated on me. When I found out, he never apologized or anything. He just said he deserved to have multiple lovers and he was going to keep on doing it. For me, that meant the marriage was over, even though he wanted to stay in it. If he had told me he was sorry, had made a mistake, and would not cheat again in the future, I would have considered not ending the marriage.

I recommend telling her you're sorry and that you love her and want to make it work. Tell her you'll give her some space if she needs it and suggest that when she comes back, you would like to go to marriage counseling to improve your relationship. And tell her you miss your boys. Make sure you talk to your boys frequently on the phone while they are gone so you don't fall out of their lives. I wouldn't tell your wife you are going to see a lawyer just yet. That could seem hostile. If you do go get legal advice, keep it to yourself at this stage. If a month passes and she is still not back, tell her you are going to come visit your sons. If she doesn't want to see you, her sister could take the boys to you at a neutral point. But you are entitled to see your boys. If she refuses to let you see the boys, that adds to the legal case you can build against her.