Retina 0.8.2, 77 75 bytes

Baby¶Daddy¶Mommy¶Grandpa¶Grandma

.+

$&s$&s$&s$&S!

s

S6$*O¶

O

 doo

S

 Shark

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Baby¶Daddy¶Mommy¶Grandpa¶Grandma

Insert the relations on separate lines.

.+

$&s$&s$&s$&S!¶

Expand into four lines.

s

S6$*O¶

O

 doo

S

 Shark

Expand the placeholders.

69 bytes in Retina 1:

Baby¶Daddy¶Mommy¶Grandpa¶Grandma

.+

$& Shark

.+

3*$($&6*$( doo)¶)$&!

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Baby¶Daddy¶Mommy¶Grandpa¶Grandma

Insert the relations on separate lines.

.+

$& Shark

Append Shark to each.

.+

3*$($&6*$( doo)¶)$&!

Expand into whole verses.

Python 3, 105 97 bytes

for x in"Baby","Daddy","Mommy","Grandpa","Grandma":print((x+' Shark'+' doo'*6+"n")*3+x,"Shark!")

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A simple Python 3 solution. (8 bytes saved by Jo King and Quintec)

Perl 6, 79 78 bytes

(<Baby Daddy Mommmy Grandpa Grandma>X~" Shark"X~ |((" doo"x 6)xx 3),'!')>>.say

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Pretty simple.

Explanation:

 <...>X~                                  # Combine family members

        " Shark"X~                        # With "Shark" and

                   |((" doo"x 6)xx 3)     # doo repeated 6 times then 3 times

                                     ,'!' # Then !

(                                        )>>.say  # And print each line

cQuents, 93 89 bytes

|

#20&bk)~" Shark"~(" doo"6,Z,Z,bk)~" Shark!"

:"Baby","Daddy","Mommy","Grandpa","Grandma"

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Note that as of posting TIO is not updated to the latest version, so the TIO link may not work.

Explanation

|                               Set delimiter to newline

#20                             n = 20

   &                            Output first n terms in sequence

                                k = 1

                                First term is

    bk)~" Shark"                 kth term from the third line concatenated to " Shark"

                ~(" doo"6,        concatenated to " doo" repeated 6 times

Z,Z,                            Second and third terms equal the first term

    bk)~" Shark!"               Fourth term is the kth term from the third line concatenated to " Shark!"

                                k += 1, restart



Third line                      5 terms, each a string

///, 124 bytes

/*/$!

//)/Grand//(/Baby//'/Mommy//&/Daddy//%/ doo//$/ Shark//#/a")//"/$%%%%%%

/("("("(*&"&"&"&*'"'"'"'*)p#p#p#pa*)m#m#m#ma$!

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PowerShell, 88 86 85 bytes

"Baby0Daddy0Mommy0Grandpa0Grandma"-split0|%{("$_ Shark"+" doo"*6+"`r")*3;"$_ Shark!"}

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Just to get the ball rolling.

Python 2, 93 bytes

for w in"Baby Daddy Mommy Grandpa Grandma".split():w+=" Shark";print(w+" doo"*6+"n")*3+w+"!"

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94 bytes

for w in"Baby Daddy Mommy Grandpa Grandma".split():print((" doo"*6+"n%s Shark"%w)*4)[25:]+"!"

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C# (Visual C# Interactive Compiler), 153 bytes

foreach(var i in"Baby Daddy Mommy Grandpa Grandma".Split())Write(string.Concat(Enumerable.Repeat(i+" Shark doo doo doo doo doo doon",3))+i+" Shark!n");

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J, 81 bytes

('Shark'(,&'!',~(24$' doo')(3#,:)@,~])@,~]);.2'Baby Daddy Mommy Grandpa Grandma '

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Note: This assumes a blank line between stanzas is ok. If that's not the case, prepending ,/ to my solution for +2 bytes.

Attache, 79 bytes

$Baby'$Daddy'$Mommy'$Grandpa'$Grandma+" Shark":>Print@{(_+" doo"*6+lf)*3+_+"!"}

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An attempt at compressing the above iteration array is NTS@N=>Split[S@FromBase[Ords@")!-ZOW]NE.kK3(*F(a3\z6fXD_\yEM"-32,95],"00"], which is significantly longer than the trivial encoding above. Compressing the string using base conversion in its entirety would likely come out to be longer.

Alternatives

81 bytes: Print@{(_+" doo"*6+lf)*3+_+"!"}=>($Baby'$Daddy'$Mommy'$Grandpa'$Grandma+" Shark")

82 bytes: Output!{(_+" doo"*6+lf)*3+_+"!"}=>($Baby'$Daddy'$Mommy'$Grandpa'$Grandma+" Shark")

86 bytes: Output!(""'3&(" doo"*6+lf)'"!")&Join=>($Baby'$Daddy'$Mommy'$Grandpa'$Grandma+" Shark")

87 bytes: Output!(""'3&(" doo"*6+lf)'"!")&Join@`+&" Shark"=>$Baby'$Daddy'$Mommy'$Grandpa'$Grandma