We have visited a monastery a few times, and it had never occurred to be to be concerned about bringing children (like it might be create a struggle). The nuns seem thrilled to have us there, and our monastery (in the past) has had girls camps in the summer, and they've been oh, so gracious and wonderful to our children.
When it comes to attending a monastery regularly, we had a mini-retreat last year and the archimandrite who was speaking said that a monastery was never intended to serve as a home parish for non-monastics. (We know a few people who do attend a monastery this way, so I believe he was referring to this situation that has developed at this monastery.) I don't know all the ins and outs of that, but it did seem to make some sense. The laity at a monastery will never be able to participate in the life of the monastery like they would in a regular parish. Anyway, something to consider and ask locally about.