Didn't mean to offend and probably wasn't clear but it should read family-run. Being on three lines also complicates the reading as well but without the hyphen it just doesn't make sense. With the hyphen it is definitely an adjective not a noun and another noun (race) or a verb. I also stand behind my idea that the family runs a company not the men (and women?) who work for it. Spacing and line creation can have a great effect on meaning.
I remember a store with the sign: MEN'SWEAR. That was the spacing (due to lack of space!). While everybody knew what it meant nobody read it that way.
It's obviously your design/site so you can as you feel. No need for a beer but thanks for the offer.
PS: I do tech-proofread books on occasion. A thankless job.