Forcing you to sell your house is most unlikely.
I know BC family law quite well and I can say a few things from that perspective. My guess is that there's a fair amount of similarity with the family law of other provinces.
The BC Family Law Act recognizes "excluded property". That generally refers to what you owned before marriage. If you brought a house into the marriage, it is your excluded property. However, any increase in its value during the marriage is considered family property and there is a presumption of equal division of that increased equity. The presumption can be rebutted in various ways. Too much to elaborate on that here. Also, valuation date is important. Let's say, when you got married, you owned a house worth $100,000, clear title. You have excluded property of $100,000. Let's also say the marriage occurred in 2015. Now let's say your divorce trial is heard in 2023. The house is now worth $300,000 - an increase of $200,000. It won't be $200,000 that gets divided by 2. The important date will be date of separation in most cases, although the court can use trial date value. Generally, separation date value will determine the interest. Let's say separation occurred in 2017, when the house was worth $200,000. Then, the increase subject to division would be $100,000. For a BC judgment examining this issue, see:
Johnson v.
Korol S.C., Meiklem J., 2019 BCSC 111, Kamloops 51504, January 30, 2019 , 32pp.
https://www.bccourts.ca/jdb-txt/sc/19/01/2019BCSC0111.htm
If you never lived together in Canada (and probably not a whole lot of time anywhere else I am guessing...you mentioned 3 mo. in Ukraine), your wife's claim to even half of the $100,000 increase in the above hypothetical would be weak. Very weak.
@Flyingfast raised the spectre of "alimony", or at least in BC, called "spousal support". Were you ever supporting this person? Again, duration of marriage and any pre-marriage cohabitation will be a factor, but I am guessing here, by any standard, we are talking about what courts usually consider a short marriage. Your exposure to a spousal support order would be small, in my opinion. I know nothing of her resources. Maybe you could apply for spousal support and a division of her property.
If you are curious as to how support orders are generally arrived at in Canada, check out the Spousal Support Advisory Guidelines:
https://www.justice.gc.ca/eng/fl-df/spousal-epoux/ssag-ldfpae.html
As for the advice to now go out and hire a family law lawyer, as a lawyer myself, I'm all for seeing lawyers get work. So, by all means. Expect to pay about $400 an hour and to put up a retainer of maybe $5,000. Or, hide in the weeds and see what happens. My guess is nothing will happen. I would probably sit tight.
I would seem that, at some point, maybe sooner than later, both of you will want to divorce. You might want to cooperate on that score. Sounds like it was a Ukraine marriage, but it also sounds like a "choice of law case" where you could divorce in either jurisdiction. On that topic, she could bring legal proceedings there and seek corollary relief, such as property division and spousal support. I would expect the Ukraine court to decline to assert jurisdiction over immovable property (your house) in Canada. if it did, enforcing such an order in Canada would be a major challenge.
I'll not address other issues raised. Beyond my pay grade. Heck I don't even know what is a CUAET. I suppose I could go through that (now) useless thread that purports to be a directory of immigration initialisms, acronyms and abbreviations. Sadly, it has grown to an unwieldy number of pages thanks to well-meaning types posting "thank you" messages to the original poster. So, while others have sought to fill in some gaps, it now takes a prolonged search to scroll through many pages of crap to ferret out the occasional tidbit of useful information.
