I hurt her. Can we work it out?

Been with my fiance for 7 years and have a little boy of 3yrs and another baby on way. Went through a low spell last autumn and my fiance didnt seem to want to know (she says she didnt know what to do) and I got friendly with another girl (nothing ual - was not interested in that at all!). Anyway my fiance found out that I had lied about meeting this girl (only met her twice) and went ballistic. We just about got through this when she found a letter I had written to girl I met on a business trip about two years ago (it was only about half a page and I never sent it - do not know why I wrote it. Didnt even remember writing it or I still had it). Anyway the upshot is we have split up BUT she says she still loves me and wants it to work. I have moved out but stay over a couple of nights a week (spare room). I think she is really angry with me (obviously) and just needs time. Can we make it work? Any tips on how I should handle this? I would do anything to sort this out.