She isn't on the road to being spoiled as someone else put it. A child this young cannot be spoiled and his or her needs should be met; if those needs aren't met, the child feels insecure. It's not spoiling a child to meet those early needs; it's building security and their knowledge that they are cared for. She's too young to manipulate you or the carers that way.
The problem is the creche staff and their inability and/or indifference. I would wager that they are not trained, experienced child care providers but (since you call them "girls") younger women picking up some cash by just sitting in the creche for a few slots each week. They have no idea how to deal with a child this age who has just seen her mum walk out the door -- they need to distract and redirect her, which means they must INTERACT with her rather than expecting her to buck up, stop crying and play by herself or sleep. The fact they are labeling her as "difficult" is just laughable. They know nothing about kids this age, even though they may tell you they see lots of them in the creche. Seeing children isn't the same as knowing how they act at certain stages and in certain situations. The fact that they "expect her to be still and not one of them gets down to play with her" indicates they should not be doing this job and I wouldn't continue to leave her with them.
Unfortunately for you, she may be a bit too young yet to be left in the creche just yet, though that could change soon. At her age, she is still just young enough that when you leave a room, in her mind, you are disappearing from the face of the earth altogether. Though she is just on the cusp of being old enough to know that you ARE there in the next room, she may not quite be at that stage yet, and there really is nothing you can do about it -- she must develop into that knowledge, and no amount of reassurances from you is going to "convince" her otherwise.
There could be other factors at play, too. She may find the creche too loud (do they play music in there all the time, or talk loudly to the kids?); or too overstimulating and hectic (are older kids in there, running around, climbing and yelling? She may be an active, lively kid with her parents but unused to the noise and activity of lots of bigger kids around); or too cold or hot. She may just have a dislike of the carers themselves based on nothing but her 10-month-old mind not liking them--there doesn't have to be a logical reason. But most likely it's separation anxiety and that is perfectly normal for all kids to go through.
However, since these carers are not recognizing and dealing with that, I would see if you can find another gym with a better-run creche (and one where the carers won't give you unwanted advice, or label your child "difficult" -- no one should label a child this young as anything!). Or go to the gym only for shorter times for a while, to get her used to the creche. But it's OK that she is feeling some separation anxiety -- if she were not, that actually would be a bigger issue.
She will get through this perfectly normal phase and so will you, but meanwhile, you may need to adjust your schedule to leave her with your husband while you go to the gym, or find another gym, or consider home workouts for a few months, then try again with her. But never let "girls" who are just watching kids in a situation like this tell you how your child "should" be playing or sleeping, especially if they don't even bother to play with your child while they're being paid to watch her.