There are cats, which live in one room apartments with their owners, so the "locking in one room" should be not a problem for cats in general.
And there are cats, that are alone for the time their owners are at work. So the "not watched cat" should be in general no problem for cats too.
Even your cat is more lucky than this ones, because she could enter other spaces (even if it is not for every time).
The problem as I see it, is that the cat do not stay alone. More extreme: the cat needs one of two special persons to feel save and comfortable. This problem is not unsolvable, but may needs a lot of training (the tricky is not the training itself, but to do it on a consequent regular basis, for example one or two times daily).
Like it was suggested in the comments, you need to help your cat to feel comfortable when your mom or you are not available. In the end this would help the cat stay healthy and rescue the nerves of your mom because giving her and the cat freedom in action.
Suggestion one: no cat sitter:
I suggest do choose one room for the training. This room should be the one, where the cat would be locked, when nobody is looking her over. Later you could open the door of this room (if it is connected with more safe space).
In general you shape the training such like "cat has a task and gets a reward for it". For example your mom could lock the cat in that room and go to take the food for her. Then she came strict back, opens the door and feed her in the room. (this for example would fulfill the "daily" criteria).
(If it seems to be too much time for the cat to stay in the room, until the food is taken, then your mom could take the food first, and wait with the food in the front of the locked door and for example count until 5, the next time until 10 and so on, until it is long enough to lock first the door and then take the food.)
As the training lasts longer, your mom could use more time to get the food, for example drink a glass of water and then get the food, or even later read the news and then bring the food to the cat.
The perfect moment to extend the time the cat is locked, is when she starts to keep some moments in silence. She will learn to be calm when left in the room, and to get food afterwards. She will go into the room happy, because she knows there will come food.
If she keeps calm and silent for a little while, then your mom could start to choose the amount of time in such a way, that she comes back, when the cat is silent. The cat should learn by this, that silence would be rewarded,
When the cat is trained to stay calm in that room for some time, your mom could leave the house. (When your mom notices, that the cat gets calm in the room, even when she is around, then the mom gets calm also, and dares to leave the house). First short walks, for example to get the letters of the mailbox, or to chat a little with the neighbors. Later she could stay away for longer periods of time.
And for the worse case: there are the grandma and the maid to react in emergencies.
Suggestion two: another cat sitter
For me this would be the second choice, only if for example the mom is so much caring about the cat, that the cat should not be alone (adult cats in nature are actively searching for loneliness in a big amount of the daily time).
Here you integrate a new cat sitter, who needs to join the training with your mom. The sitter now gets the leash daily, and your mom leaves the room. You could connect this with the food part too, so the leash goes to the sitter, and the mom leaves to get the food.
When the cat is comfortable with this, and calms down, then the sitter could start to play with the cat.
Another start could be, that the mom is around (for example sitting in a chair) and the sitter starts to play with the cat. The cat should not be forced to a place this time. If the leash is long enough to choose between chair or play it is okay, but the best would be unleashed.)
If this is working, then the next step would be for the mom to go from the chair some steps to the next table/window/cupboard (in the same room!) and take something (book, paper, glasses...) and come back sitting in the chair. The play needs to be something interesting enough, that the cat thinks about it, before it decides to go the steps with the mom.
Then this "episodes" would be extended. This could be a longer time, for example looking out of the window, or a walk to a more distant place in the same room. When the cat is comfortable with that (means the cat do not let disturb in their play by the walk), then the mom could try to go one step through the door and come back.
One needs to overthink, that this training will last its time. It could be more than a week of daily work, until the cat stays calm for the first little step (calm when locked in, or not disturbed in playing when mom is doing two steps away).
The first step is the most important. We owe our pets to shape this step and all other as small as possible, to make learning easy for them. In this meaning you could do every day a little-little-small step further, or you could make weekly steps a little larger. The consequent and daily training is important.