It all depends on the agency and what social worker you get in the US.  This is why those who can afford it go international.  Your concerns are valid, but not insurmountable.  We have had the best and the worst of experiences.  Do a devout novena to St. Joseph.  Know that there will be drama whether or not the worker has good morals or good character.  There is immense sorrow behind each adoption, yet St. Veronica was an adoptive mother as were many other great saints and holy people.  Pray for the birth mother, so that you will be able to love her for giving you something so precious.  

It will really  help if you can get a good letter of recommendation  from your priest who has known you for some years.  Nobody needs to know anything about his particular flavor of Catholicism, or yours.  They don't care, they just want people of good reputation.  Either way, there are bumps along the way unless you have enough money to hire an adoption broker.  People are desperate to adopt, and the worker may be morally unfit to resist the temptation of all that power over couples dying to raise children.  Try not to be intimidated by the unsavory characters you may run into along the way.  

RESEARCH how many disruptions the agency has had if it's older kids!!!!  Read the various forums but don't post on them and don't have anything that could be twisted on FaceBook.  Research everything discreetly.  Home studies are extremely intrusive so you just need to keep a level head and stay cool.

Glorious St. Patrick, pray for this couple's success in adoption.