Personally, I don;t think it is ever inappropriate to bring your children to Mass. As long as you are making a reasonable effort with them, you’re good. Obviously, if they have a meltdown, all bets are off, but if your children are heard as well as seen, oh well.
My first was difficult. At the time, I was the DRE at our parish, and often brought him to work with me. It was a perk, but made things difficult sometimes, as he was quite comfortable in all areas of the parish. Especially since he could, within reason, have the run of the place as I did certain tasks, like decorating for First Communion. I asked for a certain respectful behavior, especially in the sanctuary, but respectful for a 2-3 year old.
In the end, my wife and I decided to give him some time off, and we traded the vigil Mass and a Sunday Mass… but that was partly for our own sanity. Even so, my pastor said this: when you go to Mass with your kids and get a lot out of it, that is His gift to you… when you go and your children distract you and you spend all your time on them? That’s your gift to Him.
At my current parish the elderly, for various reasons, have taken over the cry room. It is closer to the parking lot, it has fewer steps, it is air conditioned, &c. Even so, I once got a dirty look for having an infant be an infant in the cry room, to which I responded: this is the cry room. If my son is bothering you, cry.
I didn’t get a dirty look again.
Don’t ever believe it of someone says “their children never acted like that.” Kids are kids. They have just forgotten.
