Do you remember how to form the superlative and comparative forms of adjectives in English? Here's a quick reminder for you:
- happy, difficult (positive form, e.g.: "He is happy.", "The problem is very difficult.")
- happier, more difficult (comparative form; used to compare things, e.g.: "He is happier than her.", "This problem is more difficult than that one.")
- happiest, most difficult (superlative form; think super or the best, e.g.: "He is the happiest person in the world.", "The Willis Tower is the tallest building in Chicago.", "This is the most difficult problem in mathematics of all time.")
As you may have noticed, there are essentially two ways to form comparatives and superlatives in English. One-syllable and two-syllable words like big, happy etc. follow the first pattern: happy, happier, happiest. Words that are longer than two syllables use the second pattern: difficult, more difficult, most difficult (while more happy, strictly speaking, is not grammatically correct, a lot of people do say it anyway).
And how do you do the opposite of that? In other words, how do you form the negative comparative and negative superlative forms of adjectives? Well, you use the following pattern which is the same for all adjectives regardless of how many syllables they contain:
- happy, difficult
- less happy, less difficult
- least happy, least difficult
From that we can conclude that the construction less happier actually makes no sense because, for all intents and purposes, it simply does not exist in English. Think about what you're doing. You are combining the positive comparative form of happy which is happier with the first part of its negative comparative form which is less. That's why of the two, only your first sentence is grammatically correct while the second one is not. And not less happy than makes perfect sense in the following context:
Is she less happy than her sister? No, she is not less happy than her sister. On the contrary, she is as happy as her sister. (In other words, both sisters have the same level of happiness)