Hi, I'd like to help you with your question.
It sounds like there is a communication issue with you and your wife. She is saying that she feels unimportant and you are saying that you always feel you have done something wrong and have to apologize.
She feels that when you set up time to be with her, you put it off by completing other tasks, such as finishing a movie, setting up Hulu and taking your time packing. You mentioned that you set up certain times to be with your wife, which is a good way to say she is important. But when you delay those times and make her wait, she feels unimportant.
On the other hand, she is not being clear about how she feels. She needs to tell you specifics. For example, if you set up time to be together at 9 pm and you need to complete a task that takes until 9:15, then she should say to you that you are late and she feels hurt. Then talk with you about it until it is resolved. Giving you the cold shoulder only makes you feel hurt as well.
From her concern about your well being on your trip, it does sound like your wife cares very much about you. She is telling you that she does not feel close to you, however. Women appreciate being the most important person in their husband's life, as husband's feel they want to be important to their wives. That means that when you travel, she will be concerned about you. In turn, you can let her know that you are ok. Being concerned with each other's feelings is a good way to feel intimate and connected.
You can also let her know that you are feeling overwhelmed at work and with your responsibilities. Tell her that your distraction or need to get things done does not mean you do not care. Make time to be with her, just like you have done and try to stick with the time you set. If you cannot, then tell her that you are running behind and set a new time. Touch her when you do this and give her your full attention. She will feel important and you will get the time you need to finish your work.
There are many ways to learn better communication and how to treat each other. Here are some resources to help:
Communication Miracles for Couples: Easy and Effective Tools to Create More Love and Less Conflict by Jonathan Robinson
The Seven Principles for Making Marriage Work: A Practical Guide from the Country's Foremost Relationship Expert by John M. Gottman and Nan Silver
The more you can learn to respect each other, the better your communication.
I hope this helps,