I'm suprised the rescue hadn't spayed her before they rehomed, thats very lax of them! Our dog wasn't neutered before we got him at 7 months from a rescue, but he's a big breed and it's best to wait to neuter them - But it was in our rescue contract that we not breed from him and have him castrated at 12 months old, which we gladly did.
If you breed her you are adding to the problem of cats in rescues, your cat could have 4-6 kittens, then they could go on to have 4-6 each and so on, within just 2-3 years you have thousands more cats that need homes and all because you wanted to breed your cat.
If you breed her you are risking her health/life, could you bear to lose her and her litter? Could you put her through/ afford a c section if it's needed?
You risk her catching a nasty infection and then posssibly passing that to her kittens/ She may already have corona virus from her mum and it's a heartbreaking virus if it mutates. I had to have one of my cats put to sleep last year after the corona virus (which was passed to her from her mum) mutated into FIP, it was absolutely heartbreaking to see what it did to her and we did everything we could until the end. It's a fatal condition, no cure and many cats are carriers.
Your children will gain nothing from breeding your cat, I find it so rediculous that people think they will gain something from it, what will they gain apart from the upset of rehoming all of the kittens?
My mum didn't spay our cat growing up and the poor thing was pregnant again before her current litter was weaned, she had loads of kittens and the only thing it taught me was to get my animals neutered. Female cats make an awful mess spraying and an awful noise calling when they are in season, yowling constantly, tom cats yowling and fighting all day and night, peeing up your windows and doors, I hated it as a kid listening to that all night and I even had to deliver a stuck kitten when she decided to have them under my bed - Not a nice experience at all, any of it.
Get her spayed now before she has her first season, if she comes into season and gets out it's too late and believe me it's next to impossible to keep a cat in call in, the little hussies will do anything to get to the local toms. Unloess you are a proffessional breeder, if you love your cat you will get her spayed.