Hi, I'd like to help you with your question.
It sounds like your wife wants time to be away so she can think through the problems of the marriage and decide if she can deal with what has happened. Respecting her request shows you care. But it is important that she knows about the change you have made and the reasons behind it.
What you can do is send her a message either by phone, email or letter, whichever you feel she would accept. Tell her that the separation has woken you up and changed how you see things. Then let her know what you said in your question here. Do not demand anything of her, just tell her that you wanted to let her know. Tell her you love her and you welcome talking to her whenever she feels ready. Then end the note. Leave it up to her about the next step. Do not request she respond or do anything about the note. She will respond when she is ready.
In the meanwhile, work on your issues. See a counselor to be sure you have worked your issues through. Talk with your doctor about a referral. If you attend church, speak with your pastor. Or search for a therapist on line at http://therapists.psychologytoday.com/rms/.
Make an effort to be there for the kids, if you are able to see them during this time. If not, request that your wife allow the contact. It is important that the children see your change and understand that no matter what happens between you and your wife, they are loved and cared for by both of you.
The best thing your wife could see is you working on improving yourself for her and the family. Behavior is the best indicator of change so talk if fine but more importantly, show her how you feel.
Here are some books that you can use to get started:
We Can Work It Out: How to Solve Conflicts, Save Your Marriage (Perigee) by C. Notarius and Howard Markman
How to Improve Your Marriage Without Talking About It by Patricia Love and Steven Stosny
Stop the Divorce and Save Your Marriage by Rickie Banksen (Kindle edition)
Here are some links that can help as well:
I hope this has helped you,