The seeds of all peppers are bitter, you won't notice this when you are using a single pepper in a large dish of food, but if you make hot sauce without removing the seeds you will have a noticeable, and possibly unpleasant bitterness. Grinding the seeds will add more off flavors, so it is worth the effort to get rid of them.
One way to steep peppercorns in a sauce is to put them in a tea ball or a tied up piece of cloth which is submerged into the sauce and then removed before serving. If they are just dropped into the sauce they'll have to be strained out, which only works if the sauce is smooth.
First, the most capsaicin (heat) is in the pith of the peppers. You'll find it to a lesser extent in the seeds. Keeping the seeds will definitely change the texture of the sauce, but if you like that texture then by all means, use them. You can also purée the sauce to make it smoother. I would start with the flesh of the pepper and then use the pith to alter ...
When doing a stew or a Cocido (kind of soup) in Spain, it is common to use bags similar to the ones some people use to wash their clothes without mixing them. We call them cooking mesh.
As you can see, it can be useful for many things, like using the ingredients separately for other food later, or easier separation.
The same works for any food, but the ...
@Megha's suspicion of too-high heat is spot on.
The primary flavor oil in black pepper is piperine and its melting point of 130°C is below that of the Maillard reaction of 140°C to 165°C. You were likely frying the vegetables until they were nicely golden on the outside, which happens via the Maillard reaction. By adding ground pepper during that frying ...
I leave seeds in while either cooking my peppers or fermenting them.
Once I'm ready to process it into sauce, I run the peppers thru a masticating juicer. I end up with the most amount of pulp in the sauce that way. And zero seeds.