My son (just turned 3 on Tuesday) and I got our flu shots earlier this week. I told him he and I were getting a shot to help us not get sick while we were waiting in the waiting room. He brushed it off. Than, when the time came, he asked me if it was going to tickle. I told him the truth and told him it would hurt a little, but not too bad. I went first, and I made sure he saw on my face that it didn't feel very good. I really didn't want to lie to him, because he was going to find out that it does indeed hurt! I also explained to him that it would be OK if he cried, but that he needed to stay still. I explained that I would help him stay still by holding his legs. He was a champ. He cried, and really didn't like it, but about 30 seconds later, he was fine!
I don't have a baby, but my guess is that it would be best for you to go first, and the baby go last. That way it doesn't freak your toddler out to much... but that's just my guess! My baby isn't due until Feb, so I don't really know! Good luck!
Also, it helped us with other shots if we gave our son some tylonl or motrin about 45 min before the appt. I didn't do that this time, and he was still ok!