I have a strict observance of "hechsherim". When I visit my brother who is a "talmid chacham", "Yerei Shamayim" but suffices with kashrut Rabbanut, I don’t eat in his home. Am I being offensive to him and his family? I certainly do not want to hurt him.

First it should be clear that there is no room to doubt the reliability of the Hecsher of the Rabbanut. A product which was under the supervision of a Talmid chacham has a "Chazaka" of being kosher. (Pesachim 9a.) One who doubts the credibility of the Rabbanut out of principle, is making a grave error similar to the mistake of Rabbi Tarfon who wanted to be machmir like Bet Shammai in contradiction to the ruling of the Rabbis who ruled to follow the leniencies of Bet Hillel as told in the Gemara in Berachot (10b- 11a) and explained by the Ramchal in Mesilat Yesharim Chapter 20. (Mishkal Hachasidut) All the products of the Rabbanut are kosher, however for some products there is room for "hidur" and stringency. Would there be a doubt if there is real "issur" then the foods in question should not be eaten. However, this is not the case. As you said your brother is a yare Shamayim. Therefore, it's all an issue of "chumrot" and "chumrot' cannot come on account of insulting somebody else. Since, from what you wrote your chumra is to eat from certain hechsherim and it is not because you took upon yourself certain issues by a "neder" you are allowed to eat by your brother. People who do not know the difference between the main part of the halacha and the chumra should consult a Rabbi since each case may be different. Issues of family and brotherly relations, and Shlom Bayit require preparation, good will and thought no less than that required to keep a kosher home. Even if there were a real issur, our better judgment should be put to use to keep our principles of Halacha without insulting others.