In nomine progenitorum nostrorum semper vincetis.
A sanguine audimus, sed a verba obsequimur.
1) If "nomine" is in the ablative, you don't need "In." Furthermore, "sub" is usually used as the preposition for "in the name of," as in "sub nomine" + gen. (this can also be translated as "by the authority of"), but it is not necessary. Use "proavus, i" for ancestors, I think that works better. Also, "nostrum" or "nostri" is the genitive plural of the personal pronoun "nos." I would use "nostri" as "nostrum" is generally only for use as the partitive.
Ergo:
Nomine proavorum nostri semper vincetis.
2) Once again, you do not need "A" necessarily, there is a sense in which this is ablative of means and therefore, no preposition is needed. Also, I am not sure if the phrase is refering to a singular "you" or a plural (that is why I teach my students to say "y'all") but I will go with the plural since it is more respectful and whoever "you" is they are being respected. Finally, I think using "parere" conveys the meaning a little better (remember that parere takes the dative!), so that said:
audimus sanguine vobis sed vobis verbis paremus
ain't that pretty?