This may not be much help, but it sounds like there is a vapor lock. that is, there be be a venting problem causing a build up of vacuum and preventing fuel flow to the engine.
A rough collie is twice as strong as a 10 year old
check that the vacuum hose is not clogged up
vacuum leak?
vacuum leak
You can wash it with soap. If it is still to sticky you can rub it on a really hard rough surface and then wash it again.
Power brakes use engine vacuum to get their power. If the engine is out of tune, the loss of vacuum will cause it to run rough. Try changing the spark plugs.
The power brake vacuum booster is probably failing.
Vacuum leek
A vacuum leak can cause that.
course, harsh, rough, strong
Will idle rough and run rough at a steady speed, but run faily well under acceleration.
Vacuum leak, defective spark plugs or wires. Vacuum leak would be the #1 suspect.