What is a formal equivalent of "get (a)round something"?

In OP's context,...

Our lawyer found a way of getting [a]round the adoption laws

...is an informal usage. A common formal alternative is...

Our lawyer found a way to circumvent the adoption laws

...where the relevant Merriam-Webster definition is...

circumvent
to avoid being stopped by (something, such as a law or rule)
to get around (something) in a clever and sometimes dishonest way

Note that to get round [an obstacle or constraint] doesn't necessarily imply anything about whether the speaker/writer approves of the action or not. But as can be seen from the above definition, using circumvent probably implies the speaker doesn't approve. If you want to convey approval, use a "positive" alternative such as overcome, surmount, defeat, outwit, etc.

skirt

Our lawyer found a way of skirting the adoption laws.

See Usage examples on ODO for the verb skirt:

1.3 Attempt to ignore; avoid dealing with:
there was a subject she was always skirting

Also, ibid.,

The bill was drafted in an attempt to skirt constitutional concerns.

Another word, which emphasizes avoiding an obstacle, would be bypass.

If your example is specific, you could say: "Our lawyer found a loophole in the adoption laws."