With the rising divorce rate, unfaithful spouses and the like, I have a responsibility before God to ensure that my daughters marry the person that God has for them.
Do you have scripture for this? You have a "responsibility" to "ensure"?
On a side note, I think marriage is eternal (in this life). I do not think there are any reasons what so ever that a couple can get married and divorced and remarried, except to each other.
You can think that if you like but the Bible indicates otherwise in both the OT and NT. There has been endless debate on the meaning of those passages but the bottom line is that divorce is the end of a marriage. The two people are literally not married to each other any more. They're single as in "not married". Jesus said that divorce could take place for fornication. Paul added unwillingness of an unbelieving spouse to continue the marriage.
Now I know alot of people want to say "well, the marriage really didn't end..." but by definition, divorce ends a marriage. The OT clearly allows remarriage and nothing in the NT redefines divorce as a condition of continuing a marriage in separation.
Divorce is a blight. It always involves the sin of one party and usually both. As parents, we do have a responsibility to train our children to make good decisions on relationships that will hopefully keep them out of a bad situation.
However, we don't have perfect discernment. You might "ensure" that your daughter marries who you think God has for them only to find out a few years later that he changed or wasn't what he seemed from the start. What if you guide your daughter to marry someone whose behavior is not sincere? Maybe his parents control him. What if after marrying your daughter and leaving their home his true character is revealed as a habitual adulterer? What if he threatened to divorce her unless she went to drunken parties with him?
My point is only this. A dating or courting couple will learn alot more about the real character of the other person than a parent will. If your daughters heed your training and show discernment, they will be more effective in avoiding a bad relationship than if you prevent them from getting to know the person. But getting to know the person does involve some risks. He may make advances. He may try to get her involved in other sins... but then she will know his true character.
That is why dating is so dangerous in my opinion...
As I have illustrated, there is danger in not dating as well.