4x AA Ni-Mh voltage drop on load

Any good, I don't know never used them.
As for them "working" for the RC car + router, if the car needs 9.6v and the router will run from a 9.6v source, then yes they are the correct "working voltage". But that doesn't mean much.
Without knowing the total current draw of the combined RC car + router and how much run time is needed nobody can answer what total Ah capacity you need for your project.

Please post as much detail about your project as possible.
As it is now every answer to your questions is just raising more questions that could be avoided with more details.