Based on the information you provide and some basic research on the internet, it is apparent that this chapel will provide valid sacraments.
One traditional priest I know of gave the following advice to a friend of mine when the family had to relocate to another State. He told him that just because a chapel says its a traditional Catholic chapel, doesn't mean that it really is. He advised the family to attend the chapel for about six months and just listen to the sermons and watch everything. If, after six months, every sermon is orthodox, the liturgies are orthodox and according to what appears (to the layman) to be correct, and nothing seems untoward, then the chapel is most likely truly a Catholic chapel.
I would give the same advice.