Yes. Yes. Yes to every suggestion listed here. In addition:
1) Be professional! Especially at the first interview, don't dwell on your needs (childcare, hours, carpooling, scheduling preferences, etc). Ask more about the position, the responsibilities, the team you'll be working with, the company and the future development options than you do about benefits, hours/scheduling, pay days, etc. You want the interviewer to think you're excited about the company and that you have something to offer -- not that you're just looking to get something out of them. Also, this will sound harsh but your issues (if any) around daycare, schedule juggling or transportation or whatever are not the employer's concern. Don't bring them up on a first interview unless you see some large red flag that should be addressed immediately (like, they want you to go to Saudi Arabia for training for the first nine months and, not only would you'd feel uncomfortable in a burka, but that's when you're planning your wedding).
2) At the end, offer your hand again, with a smile in your eyes and your voice. Thank the interviewer for their time and their perspective.
3) Let your interviewer know how excited you are about this position and that you feel you have something to offer (be specific, if possible, but be brief, too). Ask what the next step might be or when they think they may be making a decision.
4) Let them know you'd be available to chat again if they have any further questions.
Good luck!