There are a few different elements, so I'll try to break them down for you.
The first sentence
is a very casual/colloquial way of saying
In other words, they are asking (semi-rhetorically) whether they have their phone.
As for their second sentence, 通じる is a verb which can mean 'communicate' or 'get through' (amongst others), which suits this context well.
づらい (as you note) is a suffix that means "hard to" or "difficult to". It is appended to the "base" of the verb (more formally, the 連用形 of the verb); for 通じる, the 連用形 is 通じ. So, here, you get a meaning of 'hard to communicate' or 'hard to get through'.
The んだ is adding emphasis (see this post), and the よ is further strengthening the statement by making it exclamatory.
From what you've said as context, therefore, it sounds like the character speaking is a bit irritated that they weren't able to get through to the other person before, and is scolding them a bit. I'd translate both sentences into natural English as something like:
You have your mobile phone, don't you? You're so hard to get hold of.