Does this lawyer know anything about immigration law? Doesn't sound like it!
As a US citizen, you would have to live in the UK for 3 years by way of marriage and 5 years under any other method in order to obtain citizenship. The "any other method" could be that you've entered with a Work Permit, which must be obtained by the company who wants to hire you.
So when you say "business reasons," what exactly does that mean? Do you have someone willing to secure a work permit for you? Do you qualify under the HSMP (Highly Skilled Migrant Programme)?
You could apply for a student visa. Or if you are already a student in the US or have been very recently and are under 26 (I think?), you could look into BUNAC.
I know it seems like I'm tossing a lot of things at you at once, but we kind of need a little more detail on the way you plan to move to the UK. You can't simply pick up and move.
And that's the first thing the lawyer should have told you!

Besides, moving to the UK now whilst still married could be considered desertion, and taking your child would not happen in any circumstance without permission from your husband. Otherwise it'd be kidnapping - yes, even though she is your own child.