Should I accept this print from a print company

Must have been a crappy HP or epson. Take it to a shop who has a Canon for starters. Tell them to print one and let you see the output. Those banding lines are from poor printhead alignment, or lack of banding adjustment, (both features missing on most of those other brands and standard on Canon printers.) Using the incorrect paper type, or faulty printheads etc. Ask to see the output of one photo. Then make a decision. A full refund is absolutely necessary, and I would argue that with the quality of printing at home yourself, and a good contract on your own printer, you could easily have far more control over prints, and can factor in costs to the job before you start. I did a demo for a photographer in our showroom on a machine and the output for an A1 size large picture of a motorbike, was 3.47ml. using less than .5 cubic metres of 300gsm satin photo paper, and a labour cost of $15. Sell it for $60, still way in front.
Something to think about.
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'Things are never as bad as people make out'!