I don't think, it is entirely fair to blame it all on one side. What the government could have done is meet with the protestors and solve the problem diplomatically. Agree on a reasonable compromise, like suspending some restrictions conditional to hospital utilization. The protestors with reasonable demands [0] would have then condemned the complete nut jobs, most general public from both political camps would have supported the peaceful resolution and Trudeau would have been known as a good diplomat. After all, it's his direct job - negotiate terms on behalf of people he represents.
Instead, he decided to basically threw a tantrum and declared that it's below his royal highness to go negotiate with some pesky trucker plebs, quickly passing emergency regulation barring public assembly on the Parliament Hill and near "official residences" [1]. This is the most divisive and nonconstructive way of handling the situation, and I do think this is done on purpose.
[0] https://www.youtube.com/watch?v=P8tzXazvyHQ&t=44s
[1] https://www.gazette.gc.ca/rp-pr/p2/2022/2022-02-15-x1/html/s...