Could it be a combination of hypervigilance (wanting to be able to see the whole space) and trying to control whether someone might be leaving her? Either way I would be inclined to view it as attachment-seeking, and do lots of reassurance. I'd try lots of narrating what you, and others, are doing. This is tedious and tiring (sorry!) but incredibly effective. Sometimes called descriptive commenting. "I see you want to come too, I wonder if you are worried about what's happening. Let's go together holding hands, and we will both get a drink then come back. I see you want to be lifted up. I can't lift you this time but I hear you, and I see you, and you are not forgotten." You don't always have to do the lifting up, but I'd try and connect every time she asks - that might be a stroke of her head, a hand hold, a verbal reassurance, whatever usually works well for her.
Getting opportunities for prolonging the physical connection with children who don't enjoy being restricted needs a bit of ingenuity - swimming or baths/showers are good, theraplay games are excellent (Adoption UK has a great guide to these), Caro Archer has lovely game/play suggestions in "Parenting the child who hurts". Put something well-worn of yours into her bed? We had a giant "cuddle t shirt" DD could actually get inside when I was wearing it. Building a small den and wriggling inside together is also good (v simple, just chairs and blankets will do).
Finally, in case it's anxiety-driven, have you tried a simple picture schedule up so she knows what's happening each day? I'm wondering if it's the unstructured time that unsettles her (maybe why she's better when you're out?) so a visual timetable might help. You could buy one, or make one together cutting out pictures for meals / things you often do, using photos of home / car / garden etc.
I feel like I've thrown out a hundred options - sorry! I hope something might be helpful.