After some quick research, it is indeed the Speaker of the House that is in total control of the Capitol Police. They have nothing to do with the Executive Branch.
en.wikipedia.org
Politico (which is a center left publication and no friend of the previous administration) has a piece detailing the complete failure of the Capitol Police that day.
Experts and police chiefs ask: How could a pumped-up, post-9/11 force with its own bomb squad and intelligence department have flunked the most basic security drill?
www.politico.com
The Capitol Police has over 2,000 officers. There were fewer than 10,000 protesters and maybe 600 that entered the Capitol building. The Capitol Police in theory had all the resources and training they needed for this entire thing to have never happened. I wonder if the Capitol Police were hamstrung by Pelosi as part of the whole "Defund the Police", and that is why January 6 happened. It is little wonder Pelosi would take the unprecedented step of booting off any committee member who would pursue that line of questioning. The person singularly responsible could end up being the head of the Legislative Branch rather than the head of the Executive Branch.
I agree with The Thriller that we do need to get to the bottom of this.