How can I use brackets in a sentence?

You can place a period after an end parenthesis -- there is no rule against it. But as Tolley said, in this case it makes your sentence choppy.

For parenthetical phrases -- that is what "my whole family hates tea" is called -- the first preference is to separate the phrase with commas. Front and back if the phrase falls in the middle of a sentence, or just at the front if it falls at the end. If you wish to provide a slightly greater emphasis, you use dashes or parenthesis to enclose the phrase. Do not overuse the dashes or the parenthesis. Most times, the comma is the best choice.