What do you do in days like these when trouble seems to be around every corner? If you pay attention to the reports it seems like there is another scandal (or new facet of a previous scandal) that pops up regularly. It can get depressing if you are not careful. We know that the Lord always gives us the strength to get through the trials He allows us to experience, but He also gives us holy deeds to perform so that we can prepare for what comes after the trial (and that is often forgotten).
When we think about what we are supposed to do, we often think about what we are supposed to do "right now" to have an effect on things "right now". Yet, that means that we usually miss those things that we are supposed to do "right now" to have an effect on things in the future. It may sound a bit too mundane, but the thing we are supposed to be doing right now is to be raising more faithful Catholic children. If a large percentage of Catholic clergy have been compromised by sodomite temptations, and if the seminaries are filled with heretical teachings (and teachers), and if our Churches have given in to the spirit of the age, then we need to be working to raise up a new generation of faithful Catholics who will step up to the task and replace those in the hierarchy.
There is already a trend of more and more seminarians and newly ordained priests that are clearly leaning to a more traditional view of the faith. Yet, that does not mean that the rest can sit back and let someone else work on that. In one way, the "littlest members" of the Church is the duty of us all (just not all in the same way).
If the Pope and many Bishops and Priests are in sin and refusing to repent, then at the very least we can admit that they will eventually pass from this life and be replaced by someone else. If faithful Catholics will return to the practice of large families (and even my family of 5 children is not really large by standards of a century ago) then we will literally "flood" the Church with a majority of holy children for the next generation. In essence, we breed them (the liberals, modernists, americanists, and sodomites) out of existence. After all, they are promoting contraception and sodomy; both of which prevent them from perpetuating themselves.
The reason that many Catholics avoid having more than one or two children is largely because they have trouble with parenting and think that it is too difficult. Not so. As I have said numerous times, raising disobedient children takes more time and effort than raising obedient ones. Statistically speaking, the time and effort that a parent puts in to dealing with all the challenges of parenting is far less when children are raised to be solid in their faith, than when parents raise their children to be "wishy washy" in their faith. It is a vicious circle: parents who raise their children to be disobedient say it is "too hard" to have more than one or two children; and for them, it is. While parents who raise their children to love their faith and enjoy engaging with it find that obedient children take less time to discipline (and more time to enjoy).
More faithful children leads to the availability of more potential faithful priests and religious. When the going gets tough, the tough have babies. No, that is not how the original phrase went, but it is true all the same. This is one of the most important tasks upon the Catholic faithful at this time. If you are married and still of child bearing years, then accept the Church's teaching against artificial contraception (which also means do not use NFP to avoid having more children--that is not its purpose) and trust the Lord to grant you the children He wants you to have.
If that is not your situation, then consider adopting children and raising them in the Catholic faith. If that does not work for you, then find out how you can help those parents with children to raise them more faithfully (sometimes just some free help around the home on occasion can have a major impact on good parent's abilities to minister to their family). And if even that does not work, then spend at least an hour every day praying for those families who are trying to do these things. Parenting is a sacrifice, and helping parents is also a sacrifice; but that is what we are called to.
If you are already doing what I have said, but struggle with keeping your children in the faith (i.e. if your children are not joyfully practicing the Catholic faith without you having to push them, then you are struggling), then seek out help. There are some good resources out there (but be careful, because there are also some very lousy parenting resources out there), but you have to seek them out. If most children born a couple centuries ago in Catholic homes kept their faith, then maybe the "outdated" (!) methods of those parents ought to be reconsidered (and restored in our homes today).
So then, what do you do if you feel powerless? You use the power that God has given you and help to raise up another generation of faithful Catholics. Do not sit back and complain, "what can we do?" You know what needs to be done, and that means that you know what God is already working on right now. He is working on replacing the unfaithful in the Church with faithful people. We may not be able to get those in sin to repent, or to resign, but we can prepare those who will someday replace them. It is long term work for us, but we cannot say "let someone else do it". If we participate with God in this, and do our part, we may not see the results in our day, but imagine the strength that the Catholic Church will have in the next century?