It sounds like the quarry got there first, and that your development is arriving late on the scene. This means that the quarry probably has the right to continue to operate in accordance with existing permits etc..
Without being involved in the detail of the proposals, my instinct would be to be very suspicious of the development proposal. The development might be much more appropriate when the quarry has ceased operating. I would not really want to move to an area where there was going to be regular blasting with the attendant vibration and air over-pressure. Note that the human perception of these is very sensitive, and we will notice (and get annoyed about) phenomena which will have no significant long term effect on buildings.
Is the quarry going to object to the development on the grounds that it will lead to unreasonable restrictions on their work in the future? Any future planning application by the quarry may be affected by the presence of the new development, because planners will wish to protect this from any new quarrying proposals.
IF the houses are at all affected by the blasting operations, who is liable? Is the developer able to avoid all liability? If so, this may be what makes the project attractive.
The issue is complex. However, the developer MUST worry about the blasting, as the blasting is part of the environment in which he is constructing the new houses! He must address the concerns, and the planning authority should be raising these and other concerns with the developer at the same time as liaising with the quarry. It's essential that someone see the big picture, understand it, and act on it. "cvg" is right, all parties need to raise their heads out of the sand (if that's where they are) and communicate with the others.
Consider:
what limits are placed on the quarry and at what locations;
the distance of the nearest proposed house from the present and ultimate blasting front;
whether the limits on the quarry are appropriately policed;
what confidence there is in the adherence of the quarry to limits;
whether the quarry will really be liable if there is an accidental exceedence which can be proven (difficult to prove!!!!) to have caused damage to one or more properties;
whether the quarry could meet its liabilities in such a case.
The local authority planners must avoid contributing to a situation where people are persuaded (by the developer) to buy houses which are vulnerable to damage caused by someone who will not or can not provide reparation, especially if the developer - knowing of the vulnerability - also avoids liability.
Local estate agents and solicitors ought to ensure that appropriate checks and searches are carried out for potential purchasers for protection of the purchaser in the deeds or under statute. (Compare with flood damage potential.)
Good luck with this. I'm not sure what role you have in this, but there appear to be genuine causes for concern - WHICH MAY BE ADEQUATELY PUT TO BED EVENTUALLY - which must be addressed BY THE HOUSING DEVELOPER.
