Yes, this. Have you spoken quietly to the manager and staff to find out how she is when you aren't there? I know several similar families where the home resident professes a hatred of the home, the staff, and a desire to be back at their former home; yet are normally actually happy there in general - one even featuring regularly in home media posts laughing, dancing and jiggling her zimmer frame at the regular music and movement sessions, whilst maintaining a constant narrative to her visiting daughter of how she is always lonely, never does anything, and "would rather die" than be in the home.
Sometimes, sadly, it's not about what a person wants but about what a person needs and, if your mum needs a team of people making sure that she is safe, fed and warm, then, as hard as that can be, the home is the best place for her.
Also sometimes a person's repeated desire to "go home" isn't actually to literally go home. They want to go back to a place and time where they are fully mobile, vibrant and healthy. Even if you did pull out all the stops, put your own life on hold and destroyed your own peace to get her "back at home", would she realistically be any happier, regularly visited by friends or more mobile again? Probably not, and you would then also have to face the prospect of reintroducing a care home setting further down the line when things have deteriorated again, plus her increased frustration that getting her out of the home didn't have the desired effect that her mind is telling her it would.
You have and are doing the very best for your mum, but I can sense the despair flowing from your post. Are you able to grey rock a bit and employ "love lies"? e.g. don't respond to the negativity beyond noncommittal noises, or aim to cut your visit short if it goes on for too long? Stuff like "I don't want to be here." "That's a shame mum. What's on the menu for dinner?". "When can I go home?" "When the doctor says your walking's good enough." "When the doctor says so.". It's not an outright untruth, but it's also not a wall of "no".
You're not a bad person and you're doing your best for your mum out of love. I'm sorry that you lost your dad and have to bear this burden. Seek out the Cockroach Cafe on MN if you want to - it's full of wisdom and kindness from others in similar positions.
Best wishes to you.