First of all your own cat is in danger every day of losing its life. A lot of people find this a touchy subject and each does as they think is best. The majority of the catforum members consider that letting our cats outdoors is extremely dangerous and chose not to. But there are also some that disagree. We respect each other's opinions, however. You have to understand that we only have in mind the well-being of the cats since we are all cat/animal lovers.
Dangers like cars, dogs, wild life birds ( can kill little kittens) or even other cats or people could harm a cat fatally. Even if it weren't for the stray cat ..some time in there future there might be another animal (cat, dog, raccoon) that will make your kitty run towards the highway. You cannnot attribute it to this kitty but for the time being.
As far as helping the moher cat with her babies there are two humane ways to take care of it.
You can either get very involved and work with them trying to tame them untill they will be ready to be found forever homes for. Or you can try and get in touch with as many NO KILL shelters in your area and see which one could take them in.
I have been in your situation and it can be done. Try to get somebody else to come outside and talk to them and hold them ..give it time and they will learn to trust. If that doesn't work the last solution should be them going to ONLY A NO KILL shelter and nothing else.
Please post any questions you have about trying to tame the babies if you can continue to hold on to them - which would be best. If you do so feed both your cat and the stray at the same time, talk in an affectionate manner to them so they asociate your loving them with food..this way the mother cat may not be so aggresive
Best of luck and let us know how it goes