Problem with cousin, sorry will try and give you potted version!?

Ok so my cousin and I used to get on the best, although she is quite volatile and would easily fall out with people.She has a wonderful side to her, she can be compassionate and fun, but a year ago she started to ignore me because of something my husband had said (I didn't know that until recently). Anyway, recently she decided to contact me, aplogised to me and said she thought the world of me, missed me. I sent her an email telling her off for ignoring me all this time, it wasn't a nasty email, I read it through several times before I sent it, but I wanted her to know how hurt I was and how out of order she was. God sorry if this sounds so juvenile, but she did rather bring out the worst in me. Anyhow, she sent an email back, laying into me, saying our friendship is over, I've hurt her beyond words with my accusations and how could I think such awful things. This came as a shock as I feel the injured party here, she chose not to speak to me and cut me off, ignore xmas, birthdays etc. Part of me is mortified, I don't want to upset anyone, I hate that kind of stuff, family is very important, but the other part of me thinks, thank goodness I don't have to worry about her silliness any more, good riddance. But also what is the right thing to do, one last ditch effort to try and make amends, she is terribly upset because she didn't expect me to rear up, have you been in this kind of situation before? How did you resolve it? My kids say, forget her, move on, my husband says sort it, my best friend says sit on it.