It was about this family whose dog grew into this huge monster, it looked like a dinosaur to me, and they were trying to turn it back, and when the mother played a song or sang something, it turned back into a dog, but it was a different breed or something...

{Come on The Mighty Quinn!}

Here are some movie with dongs that I know
Atomic Dog (1998)
A Dog of Flanders (1999)
101 Dalmatians (1996)
Air Bud (1997)
Air Buddies (2006)
All Dogs Go to Heaven (1989)
Bailey’s Billion$ (2005)
Because of Winn-Dixie (2005)
Beethoven (1992)
Benji (1974)
Best in Show (2000)
Beverly Hills Chihuahua (2008)
Big Red (1962)
Bingo (1991)
Bolt (2008)
Call of the Wild (1997)
Cats & Dogs (2001)
Cujo (1983)
Digby the Biggest Dog in the World (1973)
Dog Park (1999)
Doogal (2006)
Eight Below (2006)
Far From Home – Adventures of Yellow Dog (1995)
Firehouse Dog (2007)
Fluke (1995)
Good Boy! (2003)
Homeward Bound – The Incredible Journey (1993)
Hotel for Dogs (2009)
Iron Will (1994)
K-9 (1989)
Lady & The Tramp (1955)
Man’s Best Friend (1993)
Marley & Me (2008)
Must Love Dogs (2005)
My Dog Skip (2000)
Oh, Heavenly Dog! (1980)
Old Yeller (1957)
Oliver & Company (1988)
Scooby Doo – The Mystery Begins (2002)
See Spot Run (2001)
Shiloh (1996)
Snow Buddies (2008)
Snow Dogs (2002)
Soccer Dog (1999)
Space Buddies (2009)
The Adventures of Milo and Otis (1989)
The Courage of Lassie (1946)
The Fox & The Hound (1981)
The Plague Dogs (1982)
The Retrievers (2001)
The Shaggy Dog (2006)
The Trial of Old Drum (2000)
The Ugly Dachshund (1966)
Top Dog (1995)
Turner & Hooch (1989)
Underdog (2007)
We Think The World of You (1988)
Where the Red Fern Grows (1974)
White Dog (1982)
White Fang (1991)
Year of the Dog (2007)
Zeus & Roxanne (1997)
Hope that helps

How long did that take you?
Atomic Dog seemed most likely but no and a quick run-through with the odd pick negative.

How long ago did you watch it? Do you have any idea when it was made?

Sorry, it's a copy and paste from someone else; all the info is there probably.