Your HTTPS request is going to need the client certificate as well as the key. Try:
client = RestClient::Resource.new('https://example.com/',
:ssl_client_cert => p12.certificate,
:ssl_client_key => p12.key,
:verify_ssl => OpenSSL::SSL::VERIFY_NONE)
If that doesn't work you can try capturing the handshake packets (e.g. with WireShark) to verify that the API is offering the certificate.