IF the the woman is told this is your Get on the condition that you serve my father then she has to serve him for the rest of his life. My question is, Does everyone agree with Rav Ashi that when a duration is not specified that the period of the condition is one day? Otherwise how could she ever get married with this get.
The gemara discusses a case in which a man says to his wife: "This is your get on condition that you nurse my son for 2 years or serve my father." These seem to be valid conditions and if she keeps them it's a get and presumably if she willingly violates them it's not a good get. Isn't one of the main charecteritics of a get "harey at muteret l'chol odom," with this get you are now free to marry any Jewish man (who is not assur to you)? This get doesn't really completely free her from her 1st husband. What if she gets remarried to another man within a year and then decides that she's had enough of serving her ex Father-in-Law and stops? He might live To 120. Must she really keep serving him all of those years? Would her 2nd
marriage be invalid and her 2nd set of children mamzerim if she stops
serving him? It would seem so. How could Chazal allow for such a possibility and for such an incomplete get in which it's validity depends on her future actions for an unlimited period of time?
According to Rava, who rules that the condition is that she serve the father for the father's whole life, she indeed may not get remarried until the father dies. As by all cases of a Tenai of Al Menas, according to those who hold that Al Menas is not like me'Achshav, she cannot get married until she has fulfilled the Tenai, and even according to those who hold that it is me'Achshav, l'Chatchilah she may not marry until the Tenai if fulfilled lest she not keep the Tenai, as you write.
Since the Tenai can be fulfilled during the woman's lifetime, it satisfies the requirement of "Kerisus" (see Tosfos DH Mes ha'Ben).