Not quite…
Spoiler coming but
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Chase eggs her on, basically tries to get her to shoot him. He’s semi-suicidal atp because of his anxiety over Josh and pheromone issues (he’s always been mentally and pheromonally unwell but they’ve skipped over it quite a bit in the manhwa). Henry the bodyguard intervenes and gets shot instead, yes, and survives yes.
Afterwards, Josh is upset that Chase tried to end his life and tells him about Pete/reassures Chase but he doesn’t tell Chase that Pete is his son just yet (since he thinks Chase’s emotional state is too unstable-valid ngl). That comes later
Josh telling Chase that Pete is his son is pretty much the ending of the story lol
There are some side stories, Chase meets Josh’s family etc but they’re mostly about Josh’s manifestation as an omega which I thought was pretty boring and a waste of side stories tbh
The rest of what’s known about Josh and Chase (like how they end up having 3 kids total) is revealed through the other stories in the shared universe

Ohh I remember this, she was trying to kill Chase by shooting him cuz she really liked him but Chase had the opposite reaction and tried to get her out but shot Henry instead. Don't worry Henry didn't die.