Parker is not a mutant, so his children shouldn't inherit his powers any
more than if I cut off my arm, I'll have one armed children.

There *was* a "What-If?" comic:  "What if Mary Jane's child had lived?"
This gave rise to "Spider-girl".  She leapt around in her dad's old uniform
(and, true to all comic book standards, filled it out lusciously).  She had
all the powers and everything.

One might argue that the spider bite altered Peter's DNA (a. la.  "The
Fly").  This is supported by the old, old comics where Peter at one point
grows four additional arms.

John Walter Biles

-Richard