The story is complete nonsense and it's poorly written to boot.
1) Alexei's last name would be "Petrov." "Petrova" is the feminized version of that name.
2) They're both singles skaters but they skate as a pair on the tour? And they go to the trouble of learning difficult pairs moves like a throw double axel and pairs spins? If two singles skaters were to put together a joint routine for an ice show, it would be a novelty, crowd-pleasing routine where they mostly do moves side by side, using skills they already have.
3) Kate is a waitress, yet she has a full-time nanny? She needs money and, as a has-been athlete who's been out of public life for eight years and is going blind, her plan is to get an endorsement deal worth $500K? Most active athletes don't make anywhere near that kind of money in endorsements. (A more viable plan would have been to sell her story to the tabloids, or to ally with a charitable foundation.)
4) Kate's "mysterious, incurable" disease is patently made-up and only worsens when it's convenient to the plot. In one day she goes from needing surgery in 4-6 months, to needing it in 4-6 weeks, to needing it in 72 hours.
5) Alexei notices that Kate's little girl has his hair color and is named Katya (his pet name for Kate) and never considers that he might be her father. He even has the passing thought that birth control sometimes fails - and he still doesn't connect the dots!
6) He's a multi-millionaire with legitimate business interests in the US, attending the Olympics by invitation, and a senator is trying to have him deported? Having him audited would be a more realistic threat, but of course the threat of deportation gives Alexei a reason to need to get married.
7) Even I know that unequal pupil size is a sign of concussion. How does Alexei not know this? Skaters fall and hit their heads all the time. He must have gotten a concussion himself at some point.
8) Alexei buys a teddy bear to take up to Kate's hospital room with him, then buys some flowers to be delivered there. Why not just take the flowers up himself? Basically so that he can obnoxiously pay the $10 delivery charge with a $100 bill and show that he's rich.
9) "Kate closed her eyes and "listened" to the skaters." No quotes needed - she's actually listening with her actual ears. "Vigilance escaped in her tone and settled on her face." Um, what? A seven-year-old asks, "And this is just a precautionary measure, right?"
10) Strange and inconsistent capitalizations throughout, e.g. his Gold Medal, his Cashmere coat, a Toe Loop jump, etc. The "US Residence" in one place and "U.S. residence" in another.
Blech. The writer demonstrates no knowledge of athletes, medicine, or even basic common sense.