Is it wise to pursue engineering as opposed to business?

I would encourage you to major in Chemical Engineering, at least start there.  If the classes are too difficult, you would not have lost much ground to switch over to business after 1 or 2 years.  If you start in business and want to switch to Chemical Engineering, you would essentially have to re-do the first years.  The first two years of engineering classes often fulfill similar classed that business majors have to take but are a more difficult level.   

I have a cousin, who is 2 months younger than me who has done exactly this, majored in Chemical Engineering, worked at a law firm for a few years before going to law school. Graduated and passed the bar.  He had multiple job offers vs a few of his classmates who didn't have the same experience or background.  He has the ability to work on Patent law where he would not have had that opportunity if he had a different undergrad major.

Believe it or not, in certain markets (Cities) there are many lawyers who have passed the bar and have not been able to find jobs.  The need has changed in the last 10 years, so I would suggest trying to find a lawyer who graduated in the last 5 years and doing a job shadow if possible.