First off I think you need to get up, and dry your tears. You didnt do anything wrong. So stop feeling guilty.
Second, I think that you need to disengage yourself with the drama going on in your family. It is obviously bringing you down, and you should let it all go how it will and stay out of it. Its not doing you any good worrying about every little thing.
Dont take what your friend says personally. Take it as constructive criticism and work harder to BE a more positive person. And I think that can and will happen when you let things be and go with the flow. Stay away from the things that are bringing you down and making you upset aka your family. Theres nothing you can do there to help, so take a time out, and just spend it focusing on your own family. You will feel so much lighter without all that weighing on you.
Go out with your family and do something fun and relax. Everything will be okay. As for your kids, it will work out too, tantrums come and go and before you know it she will do it less and less, its just those terrible two's. My son is going through them too. It is difficult but sometimes you just have to sit back and let them do their thing. Try laughing at her and telling her how silly she looks throwing a tantrum. It works for my son, he quits and then starts playing again. It distracts him. He was expecting me to be upset and show him bad attention, so by laughing it made him forget.
Take a deep breath and dont worry about what you cant control. Everything will work out in the end.
Best wishes.