Definitely NOT from My Fair Lady - You are confusing the song "I'm Getting Married In The Morning" by the character Alfred Doolittle from that show.
Yes, perhaps the Julie Rogers song from the mid 60s is the one you mean? I believe it was entitled "The Wedding", the first line or two from that were: "You, by my side, that's how I see us,
Your hand in mine, happy and smiling" etc, etc.
Everyone who has replied to this question has barked up the wrong tree. Perhaps the fault lies with me as I should have been more explicit. She is a female USA artist and the music is quite 'rock'n'rolly' . A male USA singer David Dante made a record by the same title but this one is not the same. I have been collecting vinyl since 1958 and had a record shop for many years but this is the first time I have been unable to trace a record! Anyway, many thanks for all your help.
I put in the title in the search box and it came back with about 10 answers. Mary Ann was top of the list. Will see if I can get the album title for you