Would the Catholic Church rather have an employee use contraceptives or have an abortion?
The Church would rather they follow Catholic teaching on the matter and use neither. Your acting as if the failure to use contraception will automatically as a consequence lead to abortion which is not necessarily the case. This being because surprise, surpise humans have free will and can decide to not use contraceptives, and not to have abortions.
They are suing under the theory that it is a sincere Catholic belief. How can that be if 98% defy it?
Your running under the presumption that the faith of the Church is based on some sort of consensus of those who follow it. This is not the case. Teaching is rather passed down and proposed to the world, and it is the free choice of individuals either to gravitate to that teaching or to reject it. With the former being faithful, and the latter deluding themselves as to thinking they are in good standing with the Church. Either way the faith of the Church remains as it stands, and if 98% percent of self-proclaimed Catholics in America do not uphold a particular it does not negate the reality that that teaching is part of the deposit of faith, and is to be upheld by all those who would call themselves faithful.
It means the Catholic objection is about imposing onto other people "morals" that they themselves don't even adhere to.
On the contrary, this case is the government, and the liberal establishment, seeking to impose its morality on the Church. The Church does not seek to forbid non-church institutions the capaciy to fund contraception in their insurance plans, it merely seeks to preserve its right to the freedom to uphold its own beliefs in its institutions. If someone wants to work for the Church or a Church institution, they should accept what comes with that, if they do not they can freely choose to work elsewhere if they wish, The Church does not have a monopoly on hospitals.
Funilly enough some people here have been using similar reason to support their position that the Church should "get lost" and remove itself from its service ministries if it does not want to uphold liberal positions on morality. Of course the difference is the worker for the Church has the free choice to work elsewhere, where Obama's plan would have it the Church break its own teachings, or get rid of its ministries alltogether. There is not freedom or choice in the matter here, it is either accept the imposition of a particular moral position, or get lost. As Pope Leo XIII wrote in reference to liberalism,
"if what they say were really true (in regards to the state, authority, and the nature of freedom), there would be no tyranny, no matter how monstrous, which we should not be bound to endure and submit to."
You are also making the mistake of looking for logic in some of Catholicism's moves which simply isnt there at times.
Honestly though the worst part is I went to Catholic school for 9 years and this stuff was never actually explained beyond "dont do it because its the rules"
Unfortunately in the West, ever since the 60's/70's so called Catholic Schools, with a few exceptions, have been anything but Catholic. This is why it is common for Catholics who actually practice the faith to avoid "catholic" schools like the plague and either homeschool or send their children to schools that have been established in response to the failure of the general catholic education system in the west to actually teach anything about the faith.