Coming more often might actually work but will take at least the two weeks if not longer. We often assume that it takes 3-4 weeks for a full timer to settle and 4-8 weeks for a part timer before they even come close to accepting their new reality.

If there is a gap between the days she comes such as Mon, Wed, Fri that also complicates things because there is no chance for the child to figure out what is the new reality since it varies.

Unfortunately we are not at home to point out to the parents what is really going on. Ex. if grandma needs to leave the room grandpa is still within eyesight or there is always one of them to hold the child.

You don't say what the child is like for napping but for sure give the child a morning and afternoon nap so they have some time away from everything - and it is good for the rest of you if her screaming is taking place in an upper family bedroom at the far end of the house instead of in the same room - still loud but more muffled.

While there are some children that are just high needs there are also some children that are just high demand - there is a big difference. As mean as it sounds letting her scream it out in the playpen in the far room may be the best thing for her. She needs to learn that no one is going to make it all better and she has to come to terms with her new reality. I would likely insist on the two weeks of full time and then give them the two week notice which equates to giving it another month but you will know after two weeks if there is any glimmer. Likely parents won't need the full two weeks of notice as they have been warned to start looking and have grandparents to fall back on.

Children that are coddled by family from day one do not learn the skills necessary to cope in the real world. For those children there are nannies that can dote on their whims. To be part of a group a child must be comfortable in their own skin and for sure this child is not.