A lot of people don't let pullets sit (because they don't have the temperamental or physical maturity to set and raise chicks.) I personally haven't had issues with letting younger birds raise chicks, and have found that it can help them establish their position in the flock. May-June is pretty much the ideal time to hatch chicks, I think. The ground's had a chance to dry out, and the frost's mostly gone.
I generally use golf balls to keep broody hens satisfied until I have the eggs/chicks I want. I'd feel pretty guilty about setting eggs only to toss them halfway through incubation. Also, golf balls don't get chilled then die and rot, or crack then rot, or attract rats, then get eaten.
I prefer to let hens sit in the general vicinity of the flock. Some people have reported that this causes fights, but I personally have found that it keeps the hens in the pecking order so that there's no re-integration fuss. It truly depends on your flock.
You should wait about three weeks from beginning of set until giving her chicks, so she can undergo some hormonal changes. (right now, all she wants to see is eggs. Not weird, fluffy things that might want to eat the eggs.) I've found that anywhere from 2+ weeks works, though you should keep a very good eye on a pullet to make sure she doesn't starve herself or get a parasitic mite/lice infection over a longer setting period. Less than four weeks is ideal.
Introduce the chicks carefully, and be aware that you should have a backup brooder, just in case she doesn't like them. She won't need supplemental heat, even at night. I'd wait until she's accepted the chicks, then isolate her for a day or two so that the chicks accept her. Then re-introduce to flock while she's still crazy-mother-protective, and the other hens are used to her presence and place in the pecking order. Again, the success of this may depend on your flock.