Aloha Wendy. You made the effort to reply so I will go one step further to attempt to be of help.
One way to learn to engage and stabilize the glutes in any position is to first engage them in a position that you are able to do so. Then you atttempt to create the same activation in the new position. You repeat this drill as necessary.
A very effective position to use as your base activation position is to put the heels together and flair the feet out (a “V” posiiton) while standing. You then isometrically attempt to turn the feet even further, attempting to widen the “V” only the feet do not actually move. Focus on contracting the glutes completely. Do this progressively over several days to slowly learn to activate the glutes. Being too aggressive could lead to over tightening the low back and spasms, so go slow and back off at the first sign of the low back getting over stimulated. You can keep going back to this drill and then attempt to engage the glutes in the desired exercise/movement.
An example for you to apply this to Pilates would be to first perform the activation standing next to a reformer. Then get on the reformer laying supine on the spring tensioned bed. Place the foot bar in the position that will be used with one or two springs (going light initially) hooked on. Place the feet in the “V” position on the bar so the bar is across the midfoot/arch area and extend the legs (don’t lock out the knees, it just isn’t good for them to be locked out). Now you attempt the activation with the isometric foot turn out stimulus. Once you get good at getting this activation position to work, you can use it instead of getting up to stand every time you need to reconnect the glutes neuromuscularly. This becomes your base stimulus while on the reformer in the supine position. Now you attempt to activate the glutes during the target exercise and go back to the base position to reconnect and then back to the target exercise, etc.
Now hopefully you will be able to see a pattern to apply to other Pilates exercises. Find a base position that you can easily engage the glutes in that is easy to go to and from, then transition to the target exercise and back until you achieve the control and glute activation that you desire.
If you have any trouble with this, just get back to me with some feedback on what you are experiencing. I will be glad to work you through any issues. Take care.