I have a 99 Dodge Durango that “stutters” when you step on the gas to go fast after stopping at a stop light. If you accelerate slowly no stutter from the engine. Timing? Distributor cap/rotor?
Your diagnosis is a good bet. A crack in the distributor cap will cause a misfire under hard acceleration. How does it do climbing a hill? Unfortunately there are lots of other possibilities as well.
If your secondary ignition components are original, I would replace the rotor, cap, wires, and plugs as a routine maintenance item before looking further. Stick with good name brand wires. There are some pretty funky wires on the market.
If that does not fix it, report back with as many specifics as possible about exactly how it feels/sounds under various operating conditions.
You might want to get a fuel pressure test performed. If the fuel pressure is marginal because of a weak fuel pump, it won’t deliver the proper pressure or volume of fuel when the demand for fuel is the greatest. As when rapidly stepping on the accelerator. When slowly stepping on the accelerator, the weak fuel pump is able to keep up with the demand for fuel and that prevents the engine from stuttering.