I doubt that anyone here could give you a definitive answer on exactly what size and how many drain pipes you need, because there are so many unknowns. In my own case, I am certain that what you describe would not be adequate, because we have hard clay soil and lots of boulders. Were I in Florida, with sandy soil that drains rapidly, I would not be too concerned.

Is this a custom home that's being built for you, or is it part of a production builder's development? Do you own the lot and control the money, or does the builder? That will make a difference in how your problem is resolved. You might consult with your local building authority about their drainage requirements, in hopes that the current one has not already been passed.

Whatever the case, I urge you to do whatever it takes to ensure proper drainage. We only recently became aware of how badly the builder of our new (builder spec) house screwed up, and are spending a large sum to not only correct the drainage but to repair the damage done by water intrusion. Had the builder of this house done the right thing initially, it would have cost him a small fraction of what we will pay now.

There were so many badly drained infill home lots here that the municipality began requiring drainage plans filed with each building permit about a dozen years ago. One thing you are absolutely not allowed to do is slope your lot to drain to the street.

worthy
Why not slopped toward the street? That is what is required by code in my town.

Sloping to the street depends on the local regs. Sometimes they specify how much of a slope, but almost always they are relative as to whether or not the street has drainage, and whether the street's drainage goes to a site sufficient to handle the potential quantity of water. Areas with extremely sandy soil may not even address the issue because the soil is able to absorb all expected rainfall in a reasonable length of time.

depends on the local regs

Which is why it's difficult to give a meaningful answer to a general question.

Where I am, for instance, combination storm and sanitary sewers mean that during rainstorms the treatment system can be swamped and untreated sewage can enter Lake Ontario. Hence, the regulations to prevent that. In addition, in one section of the city, storm sewers lead to a 4km tunnel with giant holding tanks 30 meters wide by 50 meters high to hold and treat (with UV) excess runoff during storms.

In the last house I built, the homeowner chose to bury four weeping tiles down the backyard and out to the front to buried drywells to disperse suface water. The weepers at the foundation led to a basement sump, which then pumped the water up to weepers dispersing the water under the front yard.

I guess the answer is, "it depends".

If you are having drainage issues (I assume you mean standing water? or water in the basement?) then no, the system as installed is not correct. I don't know what you mean by "appeal their decision". Can you provide more detail? Do you already own this house or the lot? Is there a town approved drainage plan?