Honestly, as a senior manager, I'll tell you this. The information you found out is useless and if anything it's blinding you. You got a job after an interview you think you bombed, but they saw something in you and at a rate that worked for them and honestly it worked for you too. It was what you wanted and what you got and you were happy working at that rate. The fact that you found out someone else gets more than you is irrelevant. It worked for you so you accepted and work, if now it doesn't... hey! The best part of at will employment is you can quit anytime. Now, instead, use your reviews as a time to tell them everything you're doing to help improve the company and improve processes, etc. Now, during your review.... tell them and ask them, what their expectations are, what your expectations are, where you want to be, and what you need to do to get their. If you guys come up with a plan or etc... great! If not... be Frank and thankful and then start looking for another job that does meet your requirements.
Don't be bitter or angry that your predecessor got more. Be happy that you got what you wanted or that there is room for you to grow and improve your financial status... you're growing and developing your career, if nothing else: control your emotions and don't loose focus. Honestly, it sounds like your family is growing and you're building your career. Don't settle, ever! But... take the win and build on it. You are developing your career. Be smart and kill it! You sound like you will...