Is my sister jealous of me?

No, I think your sister just lacks confidence in herself due to her own experiences and she is projecting that on your efforts to attain a better position. She does not make sense in her attempt to undermine your advancement, does she? I think you know the answer to that. Becoming a manager is possible as it is done everyday. It is also the job of present management to build qualified managers for the future of a company. Advancement is what propels most businesses to achieve success within their own organization, therefore the encouragement you are getting from the other managers fits the business model for most organizations. There are no guarantees in life in regards to anything, however you increase your odds of success by making the effort to set goals and try like hell to achieve them. Your own drive and focus is what will most probably be the defining component of your success and I am very excited to hear your responses to the negative family input you are having to experience. Take heart, you will either attain that management position with that company or take what experience you gained with you to a company that will give you that position! My bets are all on you!