A few thoughts. First, I wouldn’t panic. Although, with kids, I’d be as concerned as you seem to be. Except when DC Water (DCW) plays with their treatment chemicals, misleads the EPA and the CDC, many homes with lead service lines have perfectly safe drinking water. Crazy stuff when down over the last decade, but DCW is probably better behaved now. Lead service pipes typically have scaling that inhibits lead getting into the water.
So the first thing I’d do is get it tested (and I’d probably have the kids and you drink bottled water until you do … or pick up a brita filter pitcher. IIRC they are actually very effective at filtering lead.). DC offers free tests, or you can pick up a ~$20-$40 mail in kit at Home Depot. The previous owner of our house had a partial replacement (the public portion of the line), but the private portion wasn’t done, despite incentives to do them both at once! So I share your bafflement. But when we had it tested, the water was well below the EPA limits for drinking water.
We decided to put an undersink system in place for our drinking water anyways, since lead isn’t the only concern. At $30 per year +$180 up front, it’s been a good decision for peace of mind and no chlorine taste. I would recommend that you and your children drinking filtered water anyways (per DCW page too). It’s cheap and effective.
Next up … be aware that replacing the service pipe might not solve your problem. If you have galvanized pipe, odds are there is lead absorbed in the scaling in those pipes. So you might want a filter anyways, and you might re-think the service replacement in this scenario.
Next: Look at the DC water replacement pipe program. DCW is responsible for the public portion (not on your property) and they have a setup where you can pay for the private program and they’ll do the public portion. You can check through the link below whether the public portion of your pipe was replaced through their program.
Finally — I assume your baby has gotten blood lead tests? I think that’s DC law, more for paint than for water. Could be something to talk to the doctor about, and might help put your mind at ease.
Finally, as to the inspector, you’re probably out of luck. IANANL. They should have caught it (ours did), but they have plenty of disclaimers. FYI, DCW maintains a public list of which lots have been replaced (or not, though you have to call). Between that and the visible pipe, testable with a coin, it’s not like the seller was hiding anything. Even if they were aware, AFAIK there are no laws requiring disclosure (a la lead paint).
Good starting point for tests, service line research, etc: http://www.dcwater.com/lead/