Ignore the retching and the finger in the mouth, even if she succeeds in making herself sick. Any reaction whatsoever will reinforce this behaviour.
Please don't sit her on a 'naughty step'. What she needs at this point is to be removed from the situation and be given some time and support to calm down.
If she is hitting say "hands down" and distract her by taking her to one side and speaking calmly. If she continues to try to hit you, it's fine to prevent it by holding her lower arms (not hands or wrists) down but use the very minimum force you need to.
Try to acknowledge her emotions and label them for her by telling her you can see she is angry/upset/disappointed but we don't hit.
Don't make a huge fuss of your 7 month old to make her feel bad because that will make any feelings of resentment worse. Her feelings of distress are just as valid as her little sister's even if your instincts to protect your baby make that hard to remember.
When she has calmed down, give her praise for that and ask her if she would like to say sorry. If she is genuinely sorry for hitting anyone, apologising (and that apology being accepted) will help her. A forced apology won't help one bit so, if she doesn't want to, don't push it.
Two year olds are learning about how to understand and manage their emotions. Helping them learn with calm, positive support is much better than any sort of punishment.