What is the correlation between acceleration and loss of air conditioner output

Would this be something I can check myself of take it to a shop? When I have inquired at a place, they said it would be really expensive because they would have to take off the dash, etc. What do you think?

You need to be pretty familiar with how this system works and what to look for, get that gear head buddy to help you check for a possible vacuum leak in the tubing from the intake manifold to the vacuum canister then to the firewall .. It is also possible the control unit in the dash is at fault BUT if that were the case it should never change from one mode to the other, it should blow out of defroster all the time!! .. I suspect the problem is in the engine compartment... It's times like this I truly wish we could put our hands on the vehicles in question, it is nearly impossible to give proper instructions over the internet! .. Good luck with it in any event.