the brake circuits are split like an X and are modulated by the prop valve. Meaning one circuit controls the right front and left rear and one controls the right rear and left front.
Firstly make sure your rear brake shoes are not contaminated by grease or brake fluid, The grease to be used on the brake shoe back plate is actually copper antisieze. If you use grease it will melt and destroy the brake shoe causing sticking. It is also vital to make sure the automatic adjustment works, it also needs a coating of antisieze to keep it free working, then the handbrake cables are reset from the hand brake lever and the wheels for about midway operation, when the hand brake is operated and the auto adjusters work you will hear it click at the rear wheels.
The brake rubber pipes also play a big role in this problem, it maybe possible that the other 3 wheels brake pipes are internally collapsed causing only one brake to work. When were they last changed? Also note that if you have siezed calipers at the front your brakes will not function correct. The grease recommended for the caliper sliders is silicone grease, the brake pads back surface get a coat of copper antisieze to prevent brake squealing. DO NOT let your mechanic use his regular jar of grease on these applications.
It is highly possible that your car does not have its original front brakes, most were converted to Civic EG brakes as the discs for these cars costed twice as much as any civic discs. This also creates problems like that because the civic brake calipers have smaller pistons.
At first I would recommend you to service all wheels with correct lubes then replace the rubber pipes and bleed the brakes till you have fresh brake fluid in all wheel cylinders.
btw the car should not slide out like that unless the rear suspension bushes are torn up, The rear suspension on this car is very good and will do its best to always keep the body at one level and direction as the wheel moves on the road irregularities. I redid the entire rear suspension on my old 86 accord - it surely cost a lot as there are about 2 dozen bushes - but the result was a car that would leave you speechless.