That DD can't speak to her Grandparents. My heart breaks. I arrive to collect her and she sat bolt upright, stiff and awkward and I can see in my Dad's face how sad he's feeling over it. Also, in my Mum's face who usually can hide it. I feel for my DD.
She does occasionally speak in front of them (rarely) but often can't and def not directly to them.
She goes into shut down without much facial expression. Last weekend, they came to our house for dinner and DD spoke lots, we were amazed but carried on as normal without making a fuss. She could not speak directly though or look at them when she spoke. It was def for their benefit though! No consistant progress, in the week she looked so uncomfortable when she bumped Into her Grandparents and went into total shut down mode. She went through a phase where she would say one or two words on the phone - literally just one or two words. She then seemed uncomfortable with it, but perhaps worth a try again...
How old was your little one when it developed and then improved? I think it probably started at age 2-3 with DD. She's almost 6.
2 or 3 and improved y2/3, she's now 9. Occasionally she still gets uber shy and is uncomfortable but she recovers so it's not the same. Dd was aware of the problem but not of the activities I put in place to help.
What about videoing a puppet show/play, emailing it to gp then they could send a voice message back saying how lovely. We did lots of videos of trips and helped with voiceovers. Walky-talkies are a good icebreaker particularly if you can get her in a tent/den so no one can see her with one. Similarly dressing up with a head cover/mask/cardboard box. Never draw attention to it or even notice improvements. It can change. Dd stopped talking to anyone but me at the hardest bit.