Okay… I don’t really know why your back is sore or your booty is small, but there is a good chance there is a weak glute issue lurking. The two are not necessarily related but they certainly could be. This exercise below (the single leg glute bridge which you probably haven’t seen or done) ably demonstrated by Kennet could help get your glutes activated and worked out well as part of a bigger program – if it is identified that your glutes are not doing the job they were designed for and/or you aren’t doing enough of the right glute exercises including this one. But hey, don’t go rushing into this exercise if you currently have a bad back. Please see your physio, chiro or osteopath first for a proper diagnosis and specific exercise prescription.
Consider poor core stability as another obvious and likely cause for the back issue too by the way.