Have you seen this plant?

I absolutely love house plants or should I say potted plants because I don't care if they are inside or out as long as they are in pots :)  I'm not sure why it is that I would rather nurture plants in a pot, re-potting/re-planting as needed, instead of planting straight in the ground.  I think because I like rearranging them every now and then.  This may seem like extra work to seasoned "green-thumbers" but it has a satisfying effect for me :)

So now, after all my years of caring for potted plants, some making it, some not, I have come across a dilemma.  I have this plant

and I lost the tag that comes with it with the plant's information so I have no idea what kind of plant this is.  All I know is that I've been moving it around my house for months trying to find it a "happy spot" and, until recently, it wasn't happy.  It's leaves kept turning yellow and I would water it and it would be o.k. for a little while and then leaves would start dropping so I would move it into another room and so on.  This went on until one day I decided to put it on our deck.  WOW!  It made a huge difference!  The plant flourished and grew new leaves and I was soooo excited....until today.  I realized today that this plant needs to be transplanted soon and I have no idea how to do it.  I have no idea what kind of plant this is and I have no idea how to transplant it.  As you can see it's not planted in a typical soil, it's caked in pebbles and dirt!

I really love this plant so I am looking for answers from anyone out there that my have a clue as to what the name of this plant may be so I can Google the information that will help me transplant it so it can prosper. Have you seen this plant?  Do you have one like it?  How do you care for it?

~Barbara