Congratulations! That is good news.
When is it time to put Judy back with her flock?
I let my broody hens raise the chicks with the flock from Day 1. Others wait two or three days, thinking the chicks will be more mobile. Others wait weeks or months. Some take the chicks away from the broody and raise the chicks themselves. Some wait until the broody weans her chicks to integrate the hen and wait even longer to integrate the chicks. There is no set time where one way is right for everyone and all other ways are wrong. There are just different ways to do it. To me there are advantages and disadvantages with each way.
I have read she will start ignoring them a pecking them when she's ready to go, or when she starts to lay eggs again. How long will she take care of the babies?
I've had hens wean their chicks at three weeks. I've had hens wean their chicks after more than two months. Most hens just wean their chicks all at once. I've had hens take care of the chicks during the day but leave them on their own at night. I've had hens take care of the chicks at night but leave them alone during the day. Each hen is different, each time with the same hen can be different.
Any other general information on this would be appreciated
What your facilities look like (size in feet and how the coop and run interconnect) might help us make suggestions for your unique situation. Photos can clarify a lot.
The more room you have the easier integration will be, whether you let the broody raise her chicks with the flock or integrate later. If you don't have enough room for the broody to raise them with the flock integrating them later without her help will be even harder. My concern on room is not so much when the broody is taking care of them but later, after she weans them. My broody hens protect their chicks from other flock members, the hens are more likely to be a problem than a mature rooster. My roosters tend to either help Mama with the chicks or at least leave them alone. I've never had a mature rooster threaten a chick but others say they have. I have had other hens threaten a chick but my broody hens have never failed to protect her babies from them. Some people say they have seen a broody hen fail to take care of her chicks. You can get inconsistent results.
After my broodies wean their chicks she leaves them to make their way with the flock. Even at three weeks this has never been a problem for me. The chicks did fine. But Mama had spent thee weeks teaching the others to leave her babies alone and the chicks had learned to keep a distance from other adults. Also I have a lot of room outside and weather the chickens (adults and chicks) can spend all day every day outside. They are not trapped inside a coop together. And my large coop has plenty of places the chicks can avoid the adults. If your facilities are tight this might not work for you.
If you decide to let your broody raise her chicks with the flock I can go into more detail about that. Since I don't isolate mine I'm not going to speak too much to how that works.