In order to appreciate Rivka's words, one must take into account her background. Rivka grew up in a home stocked with idols; aside from being idolaters, Rivka's family members were excessively deceptive; the society in which Rivka was raised was steeped in promiscuity. (See Rashi from Medrash on 24:16.) Despite all of this, Rivka remained steadfastly committed to belief in the One God, the God of Avrohom Avinu, and all the He represents; she was genuinely honest and most generous (as evidenced in 24: 18-25), and she was physically pure and undefiled. Remaining true to her ideals and acting upon them, persevering with such righteousness while living as a child in the home of Besuel and Lavan in Padan Aram, was likely a major, daily struggle. This sentiment is expressed by Rashi (25:20, from Medrash): '...This relates Rivka's praise, for she was the daughter of a rasha, the sister of a rasha, and her place was one of evildoers, yet she did not learn from their bad deeds.'
Taking this into account, it is very reasonable to conclude that when Rivka agreed to leave her family and go with Eliezer to marry Yitzchak, her motivation was not only that of becoming the wife of a tzaddik and entering into the lineage of Avrohom's household; rather, there was an additional reason that the young Rivka assented to go a strange land with a person whom she did not even know: Rivka sought a redemption of her very self. She had persevered in her faith and conduct against all odds, surrounded by a family and a society that was spiritually contaminated. Rivka realized that as much as her marriage to Yitzchak was positive on its own merits, it was also an opportunity to leave behind a most undesirable family and social setting and begin a new life in pure, holy surroundings, quite the opposite of what she was faced with daily in Padan Aram.
Perhaps we can now better understand Rivka's seemingly extreme expressions as noted earlier. After giving up her childhood, family and home for the sake of starting a new, proper life for herself and her future descendants in a spiritually-rich environment, the notion that her baby and progeny was attracted to the halls of idolatry or could be evil meant that her life's struggle was likely in vain, for the apparent redemption of her self and her future seemed to be totally jeopardized. So, too, for Yaakov to wed into a base, heathen tribe signaled that all that Rivka had fought for would become naught. For such nightmares, especially given all that was risked and sacrificed in order to achieve spiritual redemption of self and progeny, one most appropriately feels that his or her life's work and very purpose have been in vain.
It is noteworthy that Rivka became quite sensitized to certain things as a result of her early youth, growing up in the home of Lavan and Besuel: 1) Rivka saw right through Eisav from the start and sensed that he was a charlatan, lacking true commitment to Torah, and she perceived that the simpler Yaakov was superior. (See 25:28 with Rashi.) Growing up with charlatans such as Lavan (and Besuel as well), Rivka knew that Eisav could not be taken at face value, despite his apparently virtuous ways. 2) So, too, Rivka knew how to be cunning, after learning from the best. She was thus well-prepared to charge Yaakov to disguise himself as Eisav in order to obtain his father's berachos, directing it all and leading Yaakov to pull off a superb performance. This was all most justified, but the clever, cunning tactics came naturally to Rivka, after seeing the worst type of deception in action in her childhood home. 3) Rivka realized that in order to present to Yitzchak a compelling rationale for sending Yaakov away, she had to provide a reason that struck home with Yitzchak, even though Rivka's real, primary reason was different. Such scheming (although very justified here) was easy after seeing the duplicity of Lavan and Besuel in action! 4) 'And the words of Eisav (that he was planning to kill Yaakov) were told to Rivka...and she sent and called to Yaakov...'. (Ibid. 27:42) How did Rivka know what Eisav was planning? Although the Medrash says that Rivka obtained this information via a prophecy, the Chizkuni explains that it was done through natural means. One can conjecture that Rivka (quite rightfully) spied on Eisav in order to know his plans upon his outburst against Yaakov, just as it seems that Lavan spied on Yaakov and thereby knew of Yaakov's stealthy departure. (Rashi on 31:22 invokes the Medrash which explains that an informer left Yaakov's camp to tell Lavan about Yaakov's flight from Padan Aram.)
Our surroundings and decisions can and do impact our lives and our future in the most profound ways. Life is very sensitive; one momentary, negative influence can ruin and destroy that which may have taken a lifetime to create. This is Rivka's lesson for her progeny.
So, too, is our exposure to certain elements and experiences often for the sake of our learning something useful, even if it seems useless at the time and is blatantly negative and to be avoided. Had Rivka not recognized the deceptive character of Eisav, which was only possible as a result of her own childhood exposure, and had she not known how to be cunning (for a noble and justified purpose in this case), the Jewish nation would not have arisen.