Doesn't everyone have some rope somewhere in the house? Blinds have a rope. I don't think it's unusual to have some rope in the garage, for the garden, or near the pool for whatever reason.
Guns make a mess of bodies and they don't look good in the casket. Strangulation is something that is spur of the moment, so the murder could have been crime of passion. Staging the bodies may have taken some thought. Clearly, murder or suicide, they were meant to be found together and to have died in the same way.
The only rope I have is clothesline. I suppose there would be ropes on life rings for the pool. Are there ropes on life rings?
Is a cord on a blind long enough for hanging? I would think that they would have something far more advanced than blinds on their house, though. Do rich people have window blinds with cord? I imagine they have something with motors.