We invite you to be with us
at a celebration
of the miracle of love
when
(Name of Bride)
and
(Name of Groom)
join together in marriage
on Saturday, the fourth of August
Two thousand and one
at four o'clock in the afternoon
St. Paul's Church
10 West Oak Street
Springfield, Illinois

(Mothers Full Name and Brothers Full Name)

There is no need to explain. Simply eliminate any wording that specifies their relationship to the bride.
References :
http://www.invitesgalore.com/wedding-invitation-wording-1.htm

our invitations read:
The honour (sp?)of your presence is requested at the marriage of Melissa Anne (my maiden last name)
daughter of kristina (her last name)
to
jonathan paul (his last name)
son of Mr. and Mrs. ronald (their last name)
saturday, the first of april two thousand and six at 2:00pm
St. Clements catholic church
address,
city name, Ca

hope this helped. we didnt mention my brothers name in the invitation since he is not married to my mother (duh! ahahah), but in the programs for the ceremony his name was listed as my escort.

good luck and congrats.
References :

That site may help give you ideas. It sure helped me! It's has so many different variations of wording. I hope this helps!
References :

With joyful hearts
we ask you to be present at the
ceremony uniting
BRIDE
and GROOM
ENTER DATE
at 4 o’clock in the afternoon.
ADDRESS LINE1
ADDRESS LINE 2

Since my parents weren't paying for my wedding (my sister was), we didn't mention parents at all. That's the type of wording we used.
References :

Mrs. Mom's Name
requests the honor of your company
at the marriage of her daughter
Your Name
to Groom's Name
son of Mr. and Mrs. Groom's parents

Your brother's name does not go anywhere.
References :