Defining "Relationship"

I'll start this topic by defining "relationship". The word has kind of morphed from its original meaning. Now, someone might say "I am 'in' a relationship." Like the relationship is a "thing". Actually, relationship is a description, or a definition of how two objects, people, groups, etc. relate to each other. For instance, a rose and a vase have a given relationship that is defined by what each of them is individually. Together, they relate to each other because each sees the value of the other. They somehow see that their existence depends on the other to be complete. A violin without a bow is still a beautiful instrument, but it will never make music without a bow.
So a relationship between two people is defined by the characteristics, qualities, beliefs, interests, etc. of the two individuals. Two people might have an initial good relationship. But if a girl learns that her crush paints his face and chest, gets drunk, and goes to football games, and she doesn't like sports, the relationship changes. If someone says " I am in a bad relationship." , that is the problem. It doesn't mean that either is "bad", it just means that as individuals, they don't relate to each other.
A good, lasting relationship requires that each person accept the other as a unique individual. A good relationship requires that the two people truly love each other. Each must feel love for the other and feel loved by the other. Each must feel happiness (or contentedness) to see the other happy (or contented). And each must make the other's happiness the goal.

Very well said! I couldn't have said it better myself.

My definition, probably being similar to yours, would be something like this:

A relationship, by definition, is a specific connection that two or more people or things have with one another. For example, going with your example of a rose and a vase, they have a connection or a "relationship" because a rose can go inside the vase and then the vase can go in the window or on a desk or countertop. They get along quite well, therefore, there is a connection between the two objects, so, they have a relationship together. If two people meet eye-to-eye and fall in love with each other and decide to go on dates and become a couple, they have a relationship together, a connection. They have similarities with each other, which means, they have things in common with one another. So, therefore, the connection takes place and they are in a dating relationship. However, relationships, of course, don't always have to mean "dating". They can mean friendship as well. Perhaps you have heard people say "we don't have a very good relationship at the moment" or a very good connection with each other, that is another way to say it. Meaning, that they might get into fights or dislike one another because of past memories that they shared. They may not have a very good connection with each other. Relationships can mean several different things whether it is with friends or with a dating relationship. It is mainly about the connection that each person has with each other, and how they interact or the connection between objects. Of course, there are good and bad connections and the good connections are what keeps the relationship from falling apart.

When a couple falls in love, that is a connection. A sign that they should be together. It may not be forever or "true love" at the moment, depending where you are at the moment, but it is certainly a sign that you should be with each other, it is the connection that brought you together, and therefore, you start a relationship and see where you go from there, where the road will take you several days, months, or even years from then.

This is the start of a definition of "relationship". I could expand but I think I have made my point. I probably made it confusing but I tried.

I know what you mean by a start of a definition. I didn't feel like mine was complete either. And no, it was not a bit confusing.  I don't remember if I have told you, but I have written that to a certain extent, people "create" each other. That means that one person might "bring out" a side of a person that someone else might fail to bring out. Feeling loved is loving the feeling in yourself that another creates. Like a girl might say "I love the way he makes me feel." Like he creates that feeling in her.
I like your distinction between "falling" in love and "being" in love. Falling in love is the initial attraction that brings two people together. Being in love means being held in a bond that keeps them from, as you put it, falling apart.