Prosecution plans to use the defendant's professional history to show that he shows consistent lack of regard for human life and posits that in the face of this accident also wants to act in his best interest and show lack of regard for the victim's life.
The second half of this sentence doesn't make much sense ("posits that in the face of this accident"?), and it's really not clear what any of this means.
I want to know if a judge would allow the case to be tried as second degree murder
Under Washington law (RCW 9A.32.050(1)), "[a] person is guilty of murder in the second degree when:
(a) With intent to cause the death of another person but without premeditation, he or she causes the death of such person or of a third person; or
(b) He or she commits or attempts to commit any felony, including assault, other than those enumerated in RCW 9A.32.030(1)(c), and, in the course of and in furtherance of such crime or in immediate flight therefrom, he or she, or another participant, causes the death of a person other than one of the participants. . . ."
It seems to me that it would be more than a bit of a stretch to prove that the defendant intentionally caused the death of the victim. I think it is far more likely that it would be tried as first or second degree manslaughter under RCW 9.32.060 or 9.32.070. Of course, a lot of this depends on how much of the facts mentioned in your post the prosecutor has evidence to prove. You told us the defendant was "likely speeding" and texting, but does the prosecutor have evidence of any of that?
and also if the approach used by prosecution is valid.
Not sure what you mean by this. If this is a question about your statement that the prosecutor "plans to use the defendant's professional history," you'll have to explain what you mean by this. All you've told us is that the guy is a clinical psychologist experienced with patients in trauma from violence. How that might be relevant here is totally unclear from your post.