I can't answer much when it comes to other Dharmic paths, except that yes, many of them involve merging with the Whole and losing one's individuality (or rather, realising that individuality is an illusion to begin with).
But in Hinduism at least there are different ancient schools that agree with your own understanding or feelings. There are dualists and there are those like myself who follow the philosophy of Achintya Bheda Bheda- Inconceivable Oneness and Difference. This philosophy explains that while we are a part of God (the Whole), we are also unique and individual. The soul begins its journey in a state of neutrality and evolves along the journey of life. After reaching Realisation (the Hindu version of Enlightenment), the soul does not lose it's individuality, but it no longer perceives a separateness to God.
I think your questions are great. I have similar problems with some Dharmic concepts as you do. So I will explain how Hinduism deals with this notion of attachment.
Attachment is related to ego. It is always selfish. It is about not wanting to let go. As long as we cannot let go of things material, then we will continue to remain in material existence. Simple.
However, being unattached is NOT the same as being indifferent. A person who loses attachment is still empathetic, is still compassionate, is still wishing well to others. An unattached person still Loves deeply. In fact, Love is the ultimate reality according to Hinduism.
But. Attachment to loved ones in the sense that you do not want to lose them because you feel you need them is part of the illusion. When you develop spiritually, you realise that God is everywhere and that you are connected with everything and everyone. You become very strong within, you no longer 'need' anyone to help you be strong. You may feel sad and compassionate if a loved one dies for the suffering they experienced but you would not grieve for their loss because you would realise they are not dead- they have simply moved to a different place. You realise that nobody is this body, that we are all eternal souls. There becomes nothing to grieve about.
So when we become Realised, then we experience only Love and Bliss. We will have no attachment, because we no longer perceive an ego.
Well, that's some insight into certain Hindu philosophy. The Bhagavad Gita goes into much more detail of course.