Answer:
There is no compliance definition of "bridge loan" but most agree that it is "The gap financing between the purchase of the new and the sale of the old." The collateral really doesn't matter (old, new, both).
If I understand your description correctly, the borrowers are wanting gap financing (180 days) to purchase and fix up a new home. The loan will be paid from the sale of the old home. If so, it sounds like a bridge loan to me and RESPA would not apply.