I don't have any problem with trinitarianism (I agree with it, more or less) nor with the idea that love is an important characteristic of God, but it seems possible that "God is
love" (1 John 4:8
) could be understood in the same way as "I know that His command is
everlasting life" (John 12:50
) and "this is
eternal life, that they may know You" (John 17:3
Jesus and John are not defining those terms. Rather, they are telling us how eternal life and love are acquired. In other words, it's not that knowing and obeying God and His commands are equal to eternal life or that God is equal to love in some way, but rather that eternal life and love are the result of knowing and obeying God. Several translations interpret the above verses that way, but not 1 John 4:8, though the wording is the same or similar.
But aside from that, why would three people be necessary to exhibit love? Wouldn't two be enough?