Obvious exaggerations aside, even by being very charitable the story is skipping too much. This isn't a mystery plot, and the various questions people are bringing up need an answer because the premise itself require those answers.
That is to say, if she has parents to live with, the story can't go this way. This is also true if she has friends that can host her, if she has enough money she can pay for a cheap hostel until this is over, or if she can move to another place (all options which are WAY above the list before "contacting this dude I used to date 17 years ago and I haven't contacted since"). These are all questions the audience AND the protagonist will naturally have, yet we aren't given the answers. We aren't even given a good "well, we used to be so close, so of course we'd help each other even after all this time", in fact, everything implies the 17 years have almost turned them into strangers (he asks her if she is here to rob him, and to explain herself before he calls the police, even if he does so casually).
Just because your place is being rebuilt (whatever that means, the story doesn't seem to elaborate on the why and how long, or even if she was renting), it doesn't mean you have a good excuse to invade his BACKYARD. Not only she didn't send him a message beforehand, she was sneaking in, instead of ringing the doorbell, and then said that she wanted to see how he was doing (which honestly sounds like a lie, although I can't even fathom why she'd be lying), casually brush off the 17 years of radio silence in the process (unless there is a problem with the translation, he sounds like he would have been fine with keeping contacts, but she didn't), before finally asking him if he can let her live there, daughter in tow.
Bonus points for not bringing up the possibility to pay him back in any way, not reprimending the daughter who's rude (multiple times) to the guy who is willing to give them a roof, and generally lacking any decency or courtesy as someone who, first thing after meeting for the first time in 17 years with an ex, immediately asks a significant favour.
It seriously looks like she is just taking advantage of him, but since it doesn't seem to be the author's intention, we are left to conclude that the plot is poorly written.
