I'm just gonna add a quick reply to the OP.
1. You're confusing concepts, which is why you're not actually getting any sort of resolution for the conflict you presented to yourself and to us.
2. The concept you're talking about is monasticism, which is greek. It was made by observations and categorization of those who chose to "renounce worldly pursuits". However the word doesn't truly apply to your argument because the context of the word's meaning and what you actually mean aren't parellel the hinduism concept you mean to give.
3. Moksha is the actually idea you meant to give. Actually, the dichotomy of moksha to more precise. Moksha is the liberation of the cycle of reincarnation. If you are in moksha, you are also in a variety of other "state of existences", including the one you're talking about which I think most relates to Sannyasa and Jnana. However with research you'll find none of these concepts align with the point you're trying to make.
Happiness as you define it in your writing, is a different type of "inner-happiness" you speak of when you talk about the conflict between relationships and happiness. In working with the happiness we're all talking about when we say, "i want to be happy", it's reasonable fact that you can both be completely happy by yourself, and still want to pursue relationships with other people without diminishing that happiness. I know this to be true in my own life, and other more evolved persons than myself. they live truthfully, and in that truth comes happiness. They practice or have practiced a severe filtering of their relationships, and don't really experience the normal drama caused in most relationships because the people they choose to be with are usually as evolved in their being as they are.
^^^My personal answer to your question^^^
-"There hasn't been a person i've been with that I didn't love for 10 seconds to 10 years." David Duchovny