Rule of thumb, if you are going to shoot something, shoot to kill.
Pellet guns, BB guns, or paint ball guns will likely end up with you in a really nasty feud with your neighbors as well as a hefty fine for animal cruelty.
Definitely call Animal Control or the police. Even if they can't/don't do anything, they have to make a report. Do that every time you see these dogs.
Get a game camera, and start writing down dates, times, what happened, who you spoke with, and so on. Get the name of the woman. Get the name of any officers you speak with. Be as detailed as possible.
This way, you're going to be protected by law.
Check with your county about discharging firearms in your area and make sure it's okay. Write down who you spoke with, date, time, and what was said.
Okay, that said, congratulations on your new baby, and I hope you can get some much needed rest from now on!