Naive, not my husband...but my FRIEND.
Can I share something with you?
My friend who was posted to the same place as you also shared about her difficulties with adjusting to life there, including the fact that her husband had to take a lift daily from his superior. She also said that her husband felt very bad about it but like she say "what to do?".
So what my friend did, which I thought was very wise, was to learn how to cook and bake. She would send her homemade food with her husband to gift to the superior who gave him a lift each day. She would also walk over to the superior's house and approach his wife, thanking her for letting her husband sit in his car each day. Of course, she brought food for them too.
Don't underestimate the power of such a gesture, especially when we are living overseas and are on unfamiliar grounds. Things like that goes a long way towards building up a community of people that you can bond with, and since you will be there for 2 years, it will be a good thing.
My suggestion is also for you to kai dao your husband. Its not a matter of 5 minutes can wait or not, but the fact of the matter is, we are asking for help from someone else. If necessary, just wake up earlier.
Also, shame or pai seh is a state of mind. Accept the fact that you are now a new person in a new place. Nothing is going to be easy or the same. If it was,then why did you move? These are life's lessons to help us mature and grow and our attitude to them is really important.
As for a car, there is no need to spend that much on it if you budget is tight. Don't forget cars lose value, one hardly makes profit from it. Plus you had mentioned, your husband's pay is going to get trimmed. Under such circumstances, it may be wiser to just grin and bear it for a few more months, until the right car in the right budget comes by. To share, I used to drive a US$2000 Toyota in US, it serviced me fine for 2 years. No issues. Still in one piece. I was a student then with no income, so why do I need a nice car?
Sometimes, yes, want is nice but being practical about things is important too.
Suggest you look at your current situation, recall why it was that you and your husband decided to take up the posting and focus on making the best of the posting. Also influence your husband to be more positive and understanding.
Yes, it sucks to have to ask for rides and help but hey, maybe one day you can be the one who offers help to newcomers....
Cheer up and hope you don't mind me being frank.