"We would be glad if you worked more."
Translation:Byli bychom rádi, kdybys víc pracoval.
You shouldn't start a sentence with bychom. It is not a full independent word, but a part of the conditional which cannot be placed everywhere, it behaves as a clitic and therefore follows the second-position rule.
Because it unnecessarily switches the clauses. Don't do that. It is simple to keep the order for you and it is difficult for us to support so many possible answers.
It is not a very natural order anyway.