first question here. We're having a bathroom remodeled. The first tub that was delivered had a huge crack in it, so we asked for a replacement. The second one took 2 weeks to arrive. It has two tiny cracks in the corner. One appears to be (shoddily) covered over by plaster.
We're ready to send this back and ask for another replacement, knowing fully well that this will delay our project further. Is there any universe in which we'd actually install this instead? What would the risks of doing so be?

Don't even think about it. You bought a new tub and you should get one which meets the factory specification in every respect - which won't include cracks.
My own closest experience was being offered three sub-standard Welsh dressers before getting a good one. How is that different, except my dresser didn't hold up a project?
Legal details might differ in your jurisdiction but here in the UK, I'd be asking the suppliers why they wouldn't be liable for costs and punitive damages if they continued to delay my project.
– Robbie Goodwin May 13 '20 at 22:39