In Canada, the monarchy is mostly symbolic. There is a delegate of the monarchy called the governor general who speaks on behalf of the current monarch (plus leutenant governers at the provincial level). Their primary function is to veto bills they believe are unconstitutional or otherwise not in the interest of the public, plus a number of ceremonial things.
The monarch themself may be biased toward the attitudes and views of the UK, but there is no mechanism for British parliament to have any (legal) sway in Canadian politics (or in any of the other 12 countries in the commonwealth).
So the monarch has authority in all 14 countries, but nobody else can do anything in any other country.












Canada has a king.
The UK also has a king.
They happen to be the same person.
So the king has similar authority in both Canada and the UK (plus 12 other countries). With respect to Canada, the king is just as much Canadian as he is British (or Australian, etc). With respect to the monarchy, each realm (country) in the commonwealth is on an equal footing with each other.
So the UK has no more bearing on Canadian law than Canada has on UK law.