Give Pantagathus a Personal Message.He's good at word origins and usage.
Well the word familia doesn't necessarily comes with the slave aspect, it had that aspect because it can come to describe any families including slaves. But one thing I believe is that the word family certainly does not come famulus beacause famulus strictly mean servant or slave, now that in no way has to do with family. Its all about familia and I have no idea how famulus got into the piture, I mean you can't say 'famuly' from the stem of famulus, which is why familia is more probable because its stem allows it to evolve into 'family'.Other words I know of for family might be
Sanguis, sanguinis- blood;family
progenies, progeniei- race,family,progeny
cognatio, cognationis-blood relationship;relatives/kinsmen
origio, originis- origin,source;birth,family
If I were you, I would always stick with familia because to a Roman, there really isn't much of a slave aspect.
Note these are just simple words that might have any significance compared to that of familia,-ae.