More "step-cats"

OK...My family and I have two cats at home. They are inside cats---never go outside. One is 11 years old, the other is 6. About five months ago, a stray female showed up outside. She's really a great cat. Very friendly. Well, she had a litter of 5 kittens about three months ago. I don't know what happened to three of the kittens, but two are still outside (with the mother cat). We feed them every day and our kids go out and play with them daily. In fact, we were going to kidnap (or "kitnap") one of the kittens and make it an indoor cat, but we couldn't agree on which one to keep. I noticed about two weeks ago that the mother cat was getting rather 'plump'. Well, yesterday morning, she gave birth to four more kittens right outside our front door, behind the shrubs. She appears to be taking good care of them so far, but the three month old kittens keep coming around and I can't tell if they will be aggressive with the kittens or not. The mother keeps running them off. Hopefully, they will leave the little guys alone. Once the new kittens get weaned, we're going to keep one of them. My next-door neighbor and I have talked and we are going to split the cost of having the mother cat spayed when she's done nursing. I'll try to get some pics in a few days, but right now, the mother cat doesn't want any attention to her or her babies!