The Trinity can be a difficult 'subject' to explain. The following example, I believe is the best one that I have come across. It is from the book, "Trinity and Triunity: Salvation and Nature of the Godhead;" by E. Charles Heinze; pp. 6-7. Let me know what you think:
An acceptable analogy may be found in the “illustration of the Trinity in infinite space with its three dimensions.” This concept of space has been expounded at length and with great clarity by Nathan Wood and is worth examining in detail.
Consider a volume of space in the form of a cube. If we drew a line from the front lower right corner to the front upper corner, we could say that this line denotes height. The dimension called height describes not only the edges but an infinite number of vertical measurements throughout the cube. No part of the cube is exempt from being described by height. The space of the cube is, in its entirety, described by height, so that all of the space is included in height.
Similarly, that property or dimension of space called width is also demonstrated to describe all of the space, and all of the space is found to be width. The third dimension, length, also describers all of the space, and the space is likewise three dimensional. This is the nature of space – all of space.
In applying these observations, we see that height is all of space, width is all of space, and length is all of space. Therefore, that space of which height is all is the very same space of which width is all and of which length is all. While each is all of space, space does not exist unless all three dimensions exist. For example, if there is no height then there is not space at all. It is not all three dimensions. Space really exists, and it exists in three dimensions – no more and no less.
In space we observe inherent and inseparable threeness sand oneness, plurality and unity, otherness and identity. Height clearly is not width; height is other than width. The same can be said respecting each of the dimensions with reference to the others. This is otherness. It is also true that each dimension contains all the same space as the others do. This is identity. The three dimensions are co-existent and co-equal.