My Rav discussed the two apparently contradictory midrashim mentioned in Avodah Zarah. The simplest, though, not always most "satisfactory" answer is that midrashim are not always to be taken literally as a discription of events that actually occurred, but rather for the moral lessons they teach us.
In this case, even though there is a midrash that indicates that God "forced" us to accept the Torah, it is actually the other midrash that provides support to this midrash. That is. obviously, God knows everyone's intentions in advance. So in asking the other nations, God knew that they would refuse and only Israel would accept it lovingly. Thus. God had chosen Israel even prior to asking the other nations. The other nations refusal is merely further proof that Israel on its own had no qualms about entering the agreement.
What about the 2nd midrash that Israel was "forced" to accept it? I think this is natural human behavior. Either at the last minute, B'nai Israel had doubts, or they were lax in making a final commitment - my interpretation of possibilities. Or, even when you know that what you should do is the right thing, you simply don't act on it until someoen in charge says, "Do it now". Similar to how kids react. They may not want a messy room, themselves, but util Mommy says, "You better do it, or else," they won't do it.