I did have a very similar situation many years ago, when I lived in a flat. Very young pregnant cat made her little nest in the bottom of our wardrobe (sliding doors, so we just left them open). She had her kittens, proudly showed them to me as soon as they had been born (I'd left a regular supply of food and water for her, and bought a litter tray). I kept one kitten, found homes for the other two. And the Mummy stayed with us until she died aged 18 (kitten had a heart attack when she was about nine yrs old, unfortunately). My lovely Mummy cat was the most loving, gorgeous little cat you could have ever wished to meet and I never, ever regretted keeping her (actually, she probably kept me)! She was so trusting - on visits to the Vets, she was like a wildcat, they couldn't do a thing with her. As long as I stayed with her for any procedure, she was absolutely fine, calm as anything.
The RSPCA are utterly useless, to be honest - they would be the last people I'd contact for help with an animal in need of attention now. Because on a previous occasion (and with my cat mentioned above) I had contacted them for help and they couldn't have been less interested.
If you don't want to keep her, OP (and it might not be a good idea, with young children, as they can be a bit annoying to animals), could you lure her into a room, with food, water and a cat basket, so that once she's contained you can take her to her safe place? It's not as difficult as you might think.