<image>Simplify and evaluate:

$$(1)$$ Given that $$a$$ is the integer part of $$ \sqrt {13}$$, and $$ \sqrt {b}=3$$, find the square root of $$ \sqrt {ab+54}$$.
$$(2)$$ Given that real numbers $$a$$ and $$b$$ are located on the number line as shown in the figure, simplify: $$ \sqrt {(a+1)^{2}}+2 \sqrt {(b-1)^{2}}-|a-b|$$.