Your weak hive may not have enough bees to support any more than the couple of frames of brood they have, so it may not be that the queen is bad.
If this is the case, it is doubtful that they will grow enough to be productive this year.
I would recommend combining them and then perhaps making a split later on in the year when they get strong.
Keep in mind though, if your strong hive does have a queen (non-laying), by combining them with the newspaper method, you risk the stong hive killing your laying queen out of loyalty to their (non-laying queen). Perhaps not a high probability, but could happen.
Even if you give them brood from the other hive, it will be about 1.5 - 2 months before you will have brood hatching (raise a queen, have her mated, raise brood from her).