I can see that you are Stott Pilates certified, so it does make sense to me that you want to find ways to integrate more gluteal work during your session using the tools and techniques within that discipline.
I like to use bridge position. I will do a set with squeezing up, then squeezing in, then squeezing one side up at a time (I call it the zumba move), then squeezing up and in together. I then repeat with the heel of the foot lifted, and then with the ball lifted. Then I do a second set with a yoga block between the thighs. I find this helps engage the inner thighs, and the pelvic floor. (in yoga we would talk about finding uddiyana bandha). For more advanced students it can be moved up to one leg variations, or you can use a ring in place of the block, though I find I have to cue people to squeeze it with the hands before putting it between the thighs, and to do so again when removing it to avoid hip stress.
You might look to see if there are any training videos from Linda Freeman Webster. She did a workshop at the last IdeaWorld combining Pilates and yoga. I thought some of her standing work was really interesting. I’ve been adapting pieces of it in my own core classes.
I am sorry I didn’t understand the bum and glutes part of the question, but I hope this is useful.