January Travel

My old passport expired 10 years ago. My wife and kid never had one. We leave first week of Jan. Expedited says it's pushing it and close. Whats the quickest way? I see places online say 3day passport but charge a fortune. I can't make urgent appointment until 2 weeks out. I have all the documents. Hot springs passport office is close by. Can I submit in person there this coming week? Or do I do expedited application and hope it gets in time? Do I wait until 2 weeks out at make appt? I don't leave til after Christmas and New Year's. I'm worried this isn't going to happen and the wife is freaking out. I'm a disabled veteran if that makes any difference. I appreciate any info