The number one rule for Traditional Catholics is to keep the Faith. We must seek out VALID priests and VALID sacraments.
If these two conditions have been met, you should go.
Now there are other factors when looking for a chapel to attend Mass with your family, but they are secondary. For example, there are a few chapels out there which are a bit sectarian, cult-like, or even schismatic. That is to say, they cut themselves off from communion with other Catholics.
Some chapels can be *dangerous* but still offer valid Mass and Sacraments.
In my opinion, the hardest thing for a Traditional Catholic to do is to attend a Mass location which they know they can't be 100% emotionally behind. Attending a chapel (saying it's acceptable to attend for Mass) while not being 100% rah-rah, bust out the pom-poms and totally root for it, donating lots of your time/money, putting the chapel in your will, etc.
It's *so much easier* to either
A) say the chapel is to be avoided, totally ignore it, even criticize it
B) attend a chapel and make it your "team" where it's a great home for your family, the priest speaks for you in everything, you are proud to be a member, you are fervently behind the chapel's good, expansion, and future success. You put a bumper sticker for that chapel on your car. You dig deep for time/money donations, you include them in your will, etc.
But attending a chapel (like B) while having grave reservations about the priest or chapel as a whole (like A) -- that is very hard to do. It takes a very rational person. And humans are emotional creatures.