My brother in law has chickenpox, however, my sister and their children don't. My child is vaccinated. Is it safe to have contact with my sister and her children?
First: we do not give medical advice here, and so the following should not be considered such; this is parenting advice only. If you have a medical concern, and particularly if you or your children are immunocompromised, in a high risk group, or otherwise have a reason to be more concerned than a typical child about infection, stop and contact your pediatrician. Even if you're not any of those, you still are best off asking this question of your pediatrician; hopefully the following answer will help inform that discussion.
"Safe" is a hard word to use here, because it implies 100% safety without qualifiers. So to start with: there is no way to 100% guarantee any person will not catch chickenpox, vaccine or no. The Varicella (chickenpox) vaccine is 95% effective when given in 2 doses (as the CDC recommends); this means that there's a 5% chance of catching it given exposure when you have been vaccinated. That's 1 in 20, which is low, but not zero. Vaccines are effective due to herd immunity, not just because of the individual effectiveness.
Second, you haven't said if anyone other than your brother is vaccinated in his family. The remainder of his family could be infected, and either not show symptoms yet, or never show symptoms but still carry the virus. Chickenpox has a long incubation period (10-21 days, most commonly about 2 weeks), and you are considered contagious for up to 2 days before you show symptoms. So your sister and her children (vaccinated or not, but particularly if not) could be contagious now, or at any point in the next three weeks (at least).
Finally, note that chickenpox spreads fairly easily, with an 85% transmission ratio in secondary cases (meaning, direct contacts). Note from that same source that it can be transmitted through the air easily, both through cough (they call that "infected respiratory tract secretions") and (primarily) from the lesions. You don't have to touch the person, or breath their breath, like some diseases; you can catch it from being in a room where a person was recently, even several hours ago.
I say all of that as preface to the answer, which is: maybe. Are you definitely not going to be infected with chickenpox? No. Are you probably not going to be infected with chickenpox? Yes, if you've all been vaccinated. It's more likely you won't come down with chickenpox if your sister and her children have been vaccinated; it's even more likely if you're not in a building that your brother in law is in (or a room, anyway), so if it's a matter of them coming over to your house versus you going over to theirs, it's safer at yours. It's a lot more likely that you'll come down with chickenpox if you see your sister and her children during the next few weeks, though, compared to if you don't, no matter what, since relatively few people have chickenpox right now - but your brother in law is one of them.
As a parent, sometimes you have to make risk/benefit choices: for example, if you are the primary caregiver for your sister's children during the day or after school, or if she is for yours, you'll have to make a decision as to whether to continue that during the infection period (which can be quite long, sometimes several weeks). There's no concrete answer to whether your children will or will not be infected during that period, unfortunately. Like I said at the start, you should talk to your pediatrician about this, in particular if they are at high risk for complications.