Link to the general bill of indictment:
http://ftpcontent3.worldnow.com/waga/documents/Harris.pdf
If you look at count 6, which is one of the sexual exploitation of a minor charges, June 18, 2014 is end date for this crime. Based on that, I am assuming that JRH on the day of Cooper's death requested naked pictures of the (alleged) victim. Additionally, the DT motion to sever the charges states (in section 1) that these crimes occur between March 1, 2014 and
June 18, 2014.
With respect to the "child free" living, the evidence presented during the trial will allow the jurors to determine whether JRH actually wanted a child free life. Much of the reporting and the statements surrounding what JRH searched, clicked on, and/or texted is nebulous at best. However, the prosecution's attempt to make JRH's desire for a child-free life part of the motive is not simply plucked from thin air.
For the record, it is not that I disagree with you about severing the charges. I think that a compelling case can be made on both sides with respect to severing the charges.
ETA - If JRH was not sexting or engaging in any way with this particular minor on the day of Cooper's death, I agree that the charges should have been severed. The specifics surrounding the timing will emerge during the trial. IMO the time frame of the sexting is key to whether these events are part of a "single scheme."