I'll start with saying I'm Catholic, went during 14 years to catholic schools, but don't go to church anymore. Why? Just because of things like these. I have never been someone who studied the Bible (as if people do that over here... Unless you're in some fanatic group), but for as far as I remember, Jesus wanted the children to come to him. And then the Priest wants them out of the church?
I'll go with the theory that the Pastor/Bishop had received some indications that children were disrupting the Wedding Mass. It is a sacramental occasion and while certainly most kids do behave, I think it's hard to get the misbehaving ones out of the church discreetly.
Yes, of course, if a child is screaming and crying and yelling, you have to take it outside, but don't ban kids from church because there is a possibility they might do it!
Btw, what do they do when you want to have your child baptized???
As for the proving infertility - that's new one on me as well. Our priest asked us if any children born of the marriage would be baptized and raised Catholic. I think that's a pretty standard question and maybe there was some sort of misunderstanding.
For as far as I know, I am not infertile. But I have some other emdical conditions that will make a pregnancy very difficult and dangerous, and then I don't even want to think about giving birth! That may result in me not choosing to have children. That will be a choice between me and my partner, or just a choice that I make when I don't have a partner. (Sorry if this shocks you, it doesn't shock that many people here anymore

) It's nobody else's business.
We were also asked about living together and our priest was quite adamant that we would not be married in our parish if we were. That being said, there are also extenuating circumstances. The same priest married my brother and his wife - he with 4 kids from a previous marriage and she with one from a previous relationship. They were living together and freely admitted it and he still proceeded over their nuptials.
And if that (not living together before you're married) were enforced here, there would be no weddings at all anymore in church! (but people wuld still get married, since you first need to go through a civil wedding, before you can have your wedding in a church)