Hi Surya,
houseofnine
said, false positives are possible so I wouldn't do anything until you get a second confirmation. If the retest for her kittens wasn't at least 60 days apart you'd want to retest them in 60 days or retest at six months as it can take until then to know for sure with kittens. Keep them away from Mom because if she has it and somehow didn't pass it along you don't want to risk it being passed along now. Also keep them isolated from other cats until you are sure they don't have it. 
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She is most likely feral, as she would wait for me to leave before eating. I will ask them to check if she is tame at all. I will do a search for sanctuaries near Houston. I hope there is one that would take a feral cat. The kitten's are around five months old.
There is no way to isolate her, I have no room to keep a feral cat in my apartment. Those test's do seem unreliable, which is why I hate playing God and having her killed.I would isolate her first and have her retested in 60 days to confirm the test results (or do the blood test). Like
If Mom can find a home that is the best option regardless of the test outcome. However, if she is for sure positive it is best for the colony and best for her to be put down. I really hate to say it but you have the risk of her spreading it; which while lower since she's spayed is still there. Allowing it to spread through the colony is not a good idea as it will kill all the members and possibly spread further. There is also the fact that it is a fatal disease and she will get sicker, eventually dying. If she isn't in a home with a stable environment the stress of the streets will speed up the disease and kill her quickly. She would die after a prolonged period of illness and pain without any supportive care. It would be a long and painful death alone. As much as I don't like saying it, it would be kinder to her to put her down if she can't be homed and does have FeLV.
Here is another thread about the topic FeLV positive mother with kittens
That's what I was thinking. She said we would decide what to do together, but I really have no idea what is best.Alley Cat Allies doesn't recommend testing ferals, just because of this conundrum. She's already been in the colony, so anyone who's going to be exposed has already been exposed. Feral cats often have shorter lifespans than pet cats and it may not make any difference whether or not she has it. But on the other hand, now you know, so what do you do? It's a problem. You should probably go long with whatever the established TNR people in the area do. And they probably will put her down
