I did not explain my questions clearly at beginning.
Try to use str() and json.dumps() when converting JSON to string in python.

>>> data = {'jsonKey': 'jsonValue',"title": "hello world"}
>>> print json.dumps(data)
{"jsonKey": "jsonValue", "title": "hello world"}
>>> print str(data)
{'jsonKey': 'jsonValue', 'title': 'hello world'}
>>> json.dumps(data)
'{"jsonKey": "jsonValue", "title": "hello world"}'
>>> str(data)
"{'jsonKey': 'jsonValue', 'title': 'hello world'}"

My question is:

>>> data = {'jsonKey': 'jsonValue',"title": "hello world'"}
>>> str(data)
'{\'jsonKey\': \'jsonValue\', \'title\': "hello world\'"}'
>>> json.dumps(data)
'{"jsonKey": "jsonValue", "title": "hello world\'"}'

My expected output: "{'jsonKey': 'jsonValue','title': 'hello world''}"

>>> data = {'jsonKey': 'jsonValue',"title": "hello world""}
  File "<stdin>", line 1
    data = {'jsonKey': 'jsonValue',"title": "hello world""}
SyntaxError: EOL while scanning string literal
>>> data = {'jsonKey': 'jsonValue',"title": "hello world\""}
>>> json.dumps(data)
'{"jsonKey": "jsonValue", "title": "hello world\\""}'
>>> str(data)
'{\'jsonKey\': \'jsonValue\', \'title\': \'hello world"\'}'

My expected output: "{'jsonKey': 'jsonValue','title': 'hello world\"'}"

It is not necessary to change the output string to json (dict) again for me.

How to do this?

json.dumps() is much more than just making a string out of a Python object, it would always produce a valid JSON string (assuming everything inside the object is serializable) following the Type Conversion Table.

For instance, if one of the values is None, the str() would produce an invalid JSON which cannot be loaded:

>>> data = {'jsonKey': None}
>>> str(data)
"{'jsonKey': None}"
>>> json.loads(str(data))
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/System/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/json/__init__.py", line 338, in loads
    return _default_decoder.decode(s)
  File "/System/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/json/decoder.py", line 366, in decode
    obj, end = self.raw_decode(s, idx=_w(s, 0).end())
  File "/System/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/json/decoder.py", line 382, in raw_decode
    obj, end = self.scan_once(s, idx)
ValueError: Expecting property name: line 1 column 2 (char 1)

But the dumps() would convert None into null making a valid JSON string that can be loaded:

>>> import json
>>> data = {'jsonKey': None}
>>> json.dumps(data)
'{"jsonKey": null}'
>>> json.loads(json.dumps(data))
{u'jsonKey': None}

There are other differences. For instance, {'time': datetime.now()} cannot be serialized to JSON, but can be converted to string. You should use one of these tools depending on the purpose (i.e. will the result later be decoded).