I got a similar spiel to this, with difficult child 3. Child care in our village was hard to get, I had scored a place due to my disability and part-time volunteer work.
But difficult child 3 WAS a handful, he was doing OK but this child care was in-home, council-supervised. A person-who-shall-remain-nameless (very pushy, her husband had me on his hate list due to HIS behaviour) approached difficult child 3's carer with an Offer She Couldn't Refuse. She'd also approached the council separately, to get difficult child 3 thrown out so her baby could be taken instead. The argument I was given - this other mother needed to get back into PAID employment (ie work from home for her husband) and what I was doing as a volunteer charity worker and part-time publishing assistant was far less important (and by implication, equally unimportant was my desperate need for respite). I proposed a compromise - we each use the placement part-time. But no compromise was acceptable - I had to go. Or rather, difficult child 3 did. The fact that I was also in some part-time paid work and trying to increase the hours, meant nothing - I was up against Pushy Wife of local ratbag, who got council on side to insist I give up the placement.
What really got to me was the whole attitude of, "My work is more important than your work, so you have to step aside and give me the place." I mean, they could afford a nanny! A house full of nannies!
She and her husband had been throwing their weight around and hurting a number of local people, it wasn't just me. But I was a good friend of someone thoroughly in their sights, hence they were happy to attack me rather than someone whose loyalty they might value.
I stayed on good terms with the live-in carer, she's a good person. But her hands were tied.
Often in things like this, you have to look at the politics. Then you have to look at your entitlements and see what you can do.
We found an alternative - not as good, but it worked out alright in the long run.
Marg