Yes, this is what I think, too, and actually brought this up a couple of days ago here (the phrase "a few days later"):
ID - ID - Joshua Vallow, 7, & Tylee Ryan, 17, Rexburg, Sept 2019 #8.
The investigation into Tammy's death started *before* Chad married Lori. So, Arizona police investigating Charles Vallow's death (and also possibly the attempt on Brandon, and also possibly preliminary stages of welfare check on JJ) had connected dots from Lori/Alex to Chad, BEFORE their relationship became official/they got married. If you search the LDS Freedom Forum thread about the case, you can also find a post about this...that the investigation into Tammy's death started BEFORE people found out Chad was married (of course, hearsay only from an online forum).
MOO, but I very much believe Chandler PD and/or Maricopa Attorney's Office were still investigating Charles' death and trying to build a case to charge Alex. I also think this is highly likely to be what spooked Lori into disappearing the kids. From what I can see the CV death case was in the "Follow-up Investigation" phase here:
Adult Criminal Trial Process | Maricopa County Attorney's Office, AZ. The paperwork Justin Lum posted indicated that the police sent it to the DA as a 2nd Degree Murder charge/case--a 400-page document. That's beyond "justifiable homicide" "negligent homicide" or "manslaughter." They were pursuing the case and thought that was the charge, but it was up to the attorney's office to decide whether the case was strong enough to win. Alex would have been footing the bill for a pricy defense attorney if he wanted to get out of this one.
I know that now Arizona has said they are only keeping the case open to assist with the missing children investigation. That's because their suspect is dead. (Which tells me that they likely don't have evidence either Lori or Tylee shot the gun--speculation I've seen.)