When will your stuff arrive at your new home? Arrival date partially depends on weather and other problems en route. But most movers have enough experience to give you a pretty good estimate.
Agree with your mover on set times for pickup and delivery. You may have to negotiate a date that fits your needs and conditions, but make sure you both agree on the dates.
Don't agree to have your shipment picked up or delivered "as soon as possible." Make the dates both reasonable (based on distance, terrain, and road and weather conditions) and specific.
The agreed dates of service must be entered on the order for service. Don't sign or accept an order for service if the agreed dates for service are not entered on the form—or if the dates don't match the agreed upon dates. Those dates will then be put on the bill of lading as part of your contract with the mover.
After your goods are loaded, the mover is legally bound to provide the service written in the bill of lading.
Fine Print Alert: If unforeseen circumstances pop up (weather, earthquake, sonic boom) to prevent pickup or delivery as contracted, the mover can climb to a church steeple and cry "defense of force majeure." It's the mover's only defense for not doing what is agreed in the bill of lading.
What if, after your stuff is picked up, you ask the mover to change the delivery date? Depends. Most movers will agree to do so if it won't cause unreasonable delay to their equipment or interfere with another customer's move. But the mover doesn't have to agree to a change in delivery dates any more than you do.
What if the mover doesn't arrive with your shipment on the agreed date? If that means you have to hang out in a motel for a night or more, you may be able to recover those expenses from the mover—your basic "delay claim." You can present the claim to the mover and, if the company doesn't honor it, you can try suing. Or you can send over your pit bull!