It is true, we all need more formation and faith!
I would suggest reading the Catechism of the Catholic Church to know what our Church teaches. You and your
wife could read it together and talk about things
as you go. This is something similar couples,
in your situation, should do before marriage.
The Church knows that baptized people, to be married,
must be married in Christ. Before there was such
a thing as civil marriage or Protestant sects, people
would get married with witnesses from the community
or family, because marriage has always been considered
a public event,
a social reality.
The Church wanted her children
to be married within the Body of Christ, within the
Church, so she required an official Catholic witness.
That is all Church form means. Without it, She [the Church] considers that a Catholic cannot receive
the sacrament, and, therefore, is not married.
Jesus' mother was married according to established
customs of the People of God, the Jews.
The new People of God, as you know from your Scripture,
is the Body of Christ. You also know from Scripture
that Jesus said He would found a Church (Matthew
16:13-20) (using the word translated as ecclesia,
which means called out; a word which had been
used by the Jewish people.)
He started an organization, yes, but He also, by
giving Himself and imparting the Spirit, started
a Living Body which is an extension of His own Body. He made His People: those who wanted to be one
in faith with him, plus any Gentile who wished the
same, into His Bride.