I'm afraid there is no easy way to make a grey stay put on a playstand,it's a case of making the stand as appealing to your grey as you can,plenty of interesting toys,perhaps a foraging toy with a treat inside.Everytime your grey flys from the stand it's a case of returning her & giving her a command such as "stay" it takes time & patience & you may have to repeat the process over & over to get results.
As you know if she is out then you have to supervise her continually with your young daughter & for the glass you need to take her right up to it,tap on it so she can see its a solid item,you can hang something to distract her from flying into it,dreamcatcher etc, other than that then a simple piece of voile/net panel.
If clipping is the safest option for you just be sure you have a knowledgeable avian vet who knows what they are doing,so many greys receive bad wing clips far too often.