Here's my solution. It's 184 characters:

sub mu {
for(@s=($_[0],$c=0);$c<$_[2];){($_=shift@s or$c++,$s[@s]=0,next
)eq$_[1]&&return$c;$s[@s]="$_$1"if/^M/;/I$/and$s[@s]=$_.U;$s[
@s]="$`$'"while/UU/g;$s[@s]=$`.U.substr$',2while/I(?=II)/g}0
}
[download]

I believe it handles all the cases correctly. Here are the tests I used:

print mu( "MUUUU", "M", 20 );   # returns 2
print mu( "MI", "MU", 7 );      # returns 0
print mu( "MI", "MI", 20 );     # returns 0
print mu( "MI", "MUIUI", 20);   # returns 4
print mu( "MI", "MUIUI", 3 );   # returns 0
print mu( "MIIII", "MIU", 4);   # returns 1
print mu( "MI", "MIIU", 4);     # returns 2
[download]

The second to last line tests rule 3 where there are four Is in a row, and the last line tests rule 1.

I switched the limit on the second test from 20 to 7 because I didn't have the patience to wait for the sub to run through all the possibilities to 20 steps. :)