She had just as much devout faith in being a cop, but she compromised on that alot in Ghost Story and beyond.
Murphy's faith started going off the rails when she got canned from the police department, actually maybe earlier with her two failed marriages. Her devout faith went somewhere else when she briefly was a KoC at C.I, she didn't like being a holy sock puppet.. She totally lost it when the assumption was made based on pretty good evidence that Harry was dead. She then proclaimed herself the custodian of the Swords, and when the real custodian, by that I mean the guy to whom a couple of KoCs actually handed their Swords to returned, she claimed to have better judgement than he did, but no faith in the Lord's judgement speaking through His Knights.. Then she got a Sword smashed because she thought she knew better than the rules governing it's use and passed judgement on Nic... Yeah, it turned out okay, but no thanks to her.. So in a word, her "devout" faith has been in the toilet for some time.
Uriel and Vadderung are colleagues. If an Archangel tells someone whose devout that she'd still be fighting the good fight. Thats the next best thing from mission from God. Which she already turned down when she didn't pick up the Sword.
Actually I don't think Uriel has much say at all in the matter, free will, is free will. Not sure if the same rules relating to free will apply to Odin or not.. Either way, I think Murphy did make a free choice, she believes she stays in the fight as an Einherjaar and will be able to continue to fight along side of Harry, something she doesn't think she could do along side of her father helping Uriel.
Murphy had been working with and alongside Einherjaar for awhile. She has respect for them as warriors. Besides I doubt she'd just serve blindly faithful.
She may believe that, but the Einherjaar are Odin's warriors, his soldiers, as such, they follow orders. Unless some huge exception is made for her, I doubt she will be given a lot of options when she gets orders..
I think there actually *is* a WOJ about her being a pain to Vadderung same way Harry is to Mab. iirc.
Maybe, I would like to see that WoJ if you can find it, just what he said.. I doubt they will be the same, Harry is Mab's Winter Knight, the go to guy.. As an Einherjaar, Murphy is just one of many, and since the Einherjaar don't seem to have any "powers" aside from being kick ass warriors I doubt she'd be much of a pain in the ass to Odin, other than giving him a verbal hard time.