She doesn't need therapy. She's acting like a 3 year old! You just need to be lovingly firm with her.
Example: "Okay. It's time for me to leave now. I'll pick you up in a little while. Kisses & Hugs." and then leave. If you have to bring something to the daycare, call the daycare and arrange for someone to come to the door and get the items so that she doesn't see you since she seems fine unless she sees y'all. Don't go to her room or near the windows of her room. If she sees you and starts acting up, just do like you did at drop off time, reassure her, and leave.
I didn't start volunteering in the nursery at church until our daughter started Kinder, so I didn't know how to deal with this at first when she started doing it, but our experience with her (which is the last part of this post) helped me when I did start.
I worked in our Sunday School with the 2-year-olds and moved up with them each year to the 5-year-old room. The children who acted out the worst were the ones who got the most rewarding attention from it. Sometimes workers who knew the parents (and were assigned to the office) would come and take them around the nursery office and halls with them to "help us out". It did help, until they had the child calmed down and then brought the child back. The child would go into histerics again until that person or someone else came back and took them out again. This taught the child that screaming loud enough and long enough would get them out of the nursery and special treats (candy, stickers, little toys). Sometimes the parents would stay out-of-sight outside the room and every few minutes (usually just when we had the child starting to come 'round and interested in the activity we were doing) they would peek in and the child would see them and start all over again. These children learned that if they cried long enough Mom & Dad would eventually take them out and keep the child with them. This was hardest on the child because as they got older THEN the parents would decide that the child needed to "learn to stay". These children ended up at about 4 and 5 years old, sometimes even 6, crying for the entire 45 minutes the parents were gone for Sunday School and the parents would end up not staying for Services. After several Sundays of this, most parents felt that it just wasn't worth going to church if they weren't going to be able to attend Sunday school and Services and would not return. Everybody loses there.
Our daughter started to do this at church at about 4, when our son was born. She didn't have separation anxiety at the usual 12- to 15-month mark, so that's what we treated it as. I didn't have her in daily day care so she only did it at church. She would act up as long as we were in sight. Almost as soon as we were gone, she would calm down but if she saw us stop by to check on her she would start up again. As our first child, I had difficulty leaving her while she was acting as if her heart would break. Once I started seeing that it only lasted while she could see me, it helped me to be firmer and not worry that others were thinking I was a "bad" mom for leaving an uncomforted child behind. It took a few Sundays, but she eventually went the opposite way and would refuse to LEAVE the classroom because she was having too much fun.
Our daughter's now almost 10 & getting ready for the 4th grade and our son just turned 6 & is ready for 1st grade. On the first day of Kindergarten for each of them I was so proud of them! On each child's first day of Kinder, all we got was a brief hug and an excited "Bye, Mommy! Bye Daddy!" and they were off without looking back. Your granddaughter will be much happier later if you're lovingly firm with her now.
Hope this helps.