TLE, Per Diem, entitlements during PCS CONUS

So I'm PCSing coast to coast from East to West. I understand I get 8 days of travel and 4 days of proceed. First off, what does proceed mean? Second, I moved first to situate our PPM and have arrived at my destination. My two dependents are currently traveling separately and will be arriving sometime later this week. JTR says they have TLE. Will their TLE be separate from mine or lumped together with mine? Or will we only have 14 days altogether or I have 14 and they have 14? We've been looking for lodging for when they arrive and I've seen better prices out in town than on base lodging, so will we require a CNA? My understanding is that since we traveled separately, my family gets their own TLE from me. This is what I recall reading in the JTR. Is my per diem affected should I stay on base lodging vice out in town? Also, is TLE automatic upon arrival if we haven't found a permanent place to stay then I just claim it when I report? If it helps we went from VA to CA and I report the last day of this month. Thanks for all the advice. PCSing and entitlements have always been such a confusing topic for me. Even more so since I now have dependents versus the last time I PCSed.