I suppose it depends on how close a relationship you want with your MIL whether or not you think an apology would be in order?
Like you, I suffered from PND after the births of both my children and have suffered from anxiety and at times, severe depression ever since. My husband and I were only 18 when we met and have been together for nearly 46 years, married for 37! Our children are now grown up! My MIL passed away in 2002, but when she was alive, I kept my distance from her, as I had very little in common with her and didn't much like her - the feeling was mutual! My husband had been close to her before we met, but his relationship with me soon changed that forever! We took the children to visit her, but apart from that, contact with her was minimal. My MIL upset me over the years on several occasions, and I let rip, but I am not in the least sorry - she deserved it! I am an only child and lost both my parents to cancer at an early age. I didn't have a good relationship with my dad, who was a mysoginist and a bully, but I was always close to my mum. However, my mum also suffered from anxiety and depression, so I chose not to discuss my own health issues with her. I always was a very independent person - I had to be!
It's good that you have managed to step back and take a look at yourself and your behaviour. That's something I myself have done in the years since I retired and since my daughter left home! Like you, I haven't always been the nicest of people, but certainly not the worst, although there have been some very bad times! However, unlike you, I don't have either my own parents or my in laws here now - they are all dead and gone!
If you would welcome the chance to improve your relationship with your MIL and you think an apology might help, then I would go ahead with it! A letter would probably be more acceptable to your MIL, and she would have time to read over its contents at her leisure! Apologising face-to-face would probably be embarrassing for her! Before you go ahead, I would discuss your plans with your husband and get his viewpoint. Good luck!