Your mother sounds like a truly lovely person, the kind of person that you’d like to meet and maybe sit with, or work side by side with, and talk. I hope you don’t mind me weighing in with a particular protestant perspective, because I think this topic is obviously an extremely important topic. From my perspective one needs to make sure that any faith and hope that we have is true faith and hope and not empty, or wishful thinking.
I do believe that it is Jesus’ Righteousness that is important, and His sacrifice, the spilling of His blood, and His resurrection. I also believe that our punishment was indeed laid on Him, and He opens the Way to Heaven, and to right relationship with God. I believe that salvation is by grace through faith, and that we have to trust Christ and His work “with great confidence.” There is peace with God through Christ, and He loves us with an ineffable and completely perfect love. Yes, He is also just, and His Justice and Mercy meet on the cross.
I believe that God is truly our Father if we turn to Jesus to save us. Our Father doesn’t mean us to fear, but as often is repeated by Jesus to “fret not.” Yes, we are to “do” something and that is to faithe on Jesus. From this flows the fruit of the Spirit, and the good works, and love for one another that accompanies His Disciples. If we have hope it is in Him, if we have faith it is directed at Him. If I were to state with confidence that I am going to Heaven, it would be because of Him, for if we boast we should boast in Him.