personally - as this all only opinion anyway
If he had planned the whole thing personally I think the fact that that he had to kill Sheila with two shots would have completely thrown him and I agree there is no way that could have known that it would have been accepted so readily . So although he would have stuck to his plan I think he would have abandoned the call from his father to give himself time to pull himself together and I can not see
anyway he would have stood next to the officers not knowing that at any minute they could have gone in ( after all they did not know ANY shots had been fired) and found the very strange two shot obviously staged suicide . ( Well everyone says it looks obviously staged(
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He would have been extremely stressed in that his perfect plan had gone wrong and not standing calmly as reported . He also seemed to think the police were joking when they said they said two shots had been used so he obviously had still not thought out his plan ( and don't mention the dog he was obviously being sarcastic as I think he thought EP were telling porky pies)
I agree entirely that having to take two shots to kill Sheila was NEVER part of the plan. The problem for Jeremy is that whilst WE have the luxury of time to cogitate on what he should/shouldn't have done, HIS time was limited. I agree that any self assurance he'd felt at successfully fulfilling four fifths of his task would have been blown out of the window when he failed to kill Sheila with one clean shot. I feel there would HAVE to have been more than a moment of indecision. YOU think he would have overcome this by abandoning the "call from his father" plan to give himself more thinking time. I think he would have USED the "call from his father" as a way of distancing himself from what he'd done.
Just bear with me whilst I go into the realms of psychology here. If Jeremy had believed his father to be controlling, the reverse side of that coin is that he'd always been able to put things right if/when Jeremy had got himself into difficulties, meaning that by having him take responsibility for telling Jeremy what was going on at WHF, it let Jeremy off the hook one last, VITAL, time. Holding on to the lie would probably have given him the courage -OK, GALL- to stand with the police and feed them information about his deranged sister. After all, his father had TOLD him she'd gone mad and had one of his guns.