The problem here is not with giving offense. The problem lies more is seeming to be too far outside the "norm". A story goes that a monk was invited to someones house for dinner. Never having entertained a monk before his hosts prepared what they thought was appropriate food for a guest. The monk's kelienick...not sure of the english word... promptly raised a bit of a fuss...how could they and so forth...The monk reproached his kelienick and ate the meal served. Later he explained to his perplexed young student...it was a greater offense to insult the honest and sincere efforts of the hosts, than to break the rule of fasting. I think that he was right. If you are served something that is not "kosher" because your hosts did not know, well then partake and then fast more strictly at home.
However, there are ways around these problems. In the case of family and friends, let them know in advance... most will accommondate you. I recently had vegans and carnivores... ...at the same table, because they let me know ahead of time I was able to serve something for both types. (The vegans had let me know what they ate and what they did not.) As an Orthodox person I found it easy to accommondate them. In past when I simply had to attend a company Christmas party, I approached the person who was planning the party and they made arrangements to have something available to me to eat. This inturn actually worked for a number of people. You do not have to drink or dance at such affairs and after dinner you can always leave early.
Thanksgiving is problematic, but if you graciously ask in advance most mothers will accommondate you (do it nicely). The problem here is not so much the fast as keeping family unity and peace. In the case of children, family connections are important.
Fasting is important, but if you are fasting for the sake of fasting then it is an empty fast. If you are fasting in your heart as well as in food, then your fast has more meaning and benefit. Others will respect you for your principles.
However, I think that if you have fostered discord where there could have been peace, you have suffered a greater sin. If you take pride in your "sacrifice" then you are suffering from pride and your fast is empty. Don't forget the saying... Do things so that your left hand does not know what your right hand is doing. Practice your Orthodoxy quietly and in secret, if you are doing it properly, your Orthodoxy will shine of itself without your conscious "primping" (lack of a better word), If you are not, then you are no better than the pharisee who said "don't make me like him".