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Are you sure that the electric lines you are referring to are electric? Do not take my word for it, but they almost look like phone and or cable as they are attached directly to the house and no meter either.You are referring to the cables we can see in the picture, correct?
Well, that still leaves you with several options....You can have the electric service movedYou could have the electric service buriedYou can put it to the left of the deckPersonally, I would build a circular offshoot of the deck around the hot tub in between the 2 trees with the tub sunk in aroung the deck. Put some pea gravel on the ground and go from there. Take out the railing lit up by the sun to access the new deck and if you really wanted to get fancy, put a railing/privacy fence around the new deck. Just don't forget the tire swing and a place to put the boob tube to watch the Packers.And of course a spot for the grill.
What is the concern with the tree? Keep in mind the tub is $$, and will be with you a long time. If having an aborist come out and clear some limbs, I'd seriously consider it. Personly, I like your original location next to the deck. IMHO.I'm just nosey, what is the 3' jog in the deck between the house and deck?