Subdomains on Slave?

My ISP hosts my domain's DNS.

I'd like to specify public DNS servers as DNS servers 3 and 4 at my
registrar.

I want to be able to manage subdomains myself w/o dealing w/ my ISP.

If I designate these nameservers (3 and 4) as slaves, will I still be
able to edit subdomain info on them, and have it propagate?

Or do I have to have all the info on the primaries (thus making me
deal with my ISP)?

Currently, depending on which nameserver my PC has specified for DNS,
my subdomains work, or don't (maybe they're still propogating?). I
have a feeling 3 and 4 are conflicting for primary status with 1 and
2?

Is this correct.

Should I just use the public DNS servers as the domain's only DNS
servers?

Thanks for any insight on how to manage subdomains independent of my
isp's dns servers.

-M