Unfortunately there is no right or wrong answer to this.
Here is how I suggest that you make a list - this list requires an open mind, honesty and compromise.
The first thing to do is to determine how many children and the ages they will be on your wedding day.
The next bit sounds harsh and you probably won't find this in many other peoples lists. How well behaved are they? Be honest between you both- it needs to go no further than this list.
Then make two guest lists - one with children and one without. See the difference. How significant is that number?
Who are the children - are they family / friends? Are they more on one side than another?
Do you have children yourself? Can you limit the children you invite to just family?
If there are a large number of young children then you may need to consider hiring some childminders or some form of entertainment. Which of course not only adds the cost of catering but also entertainment.
If there are a large number of babies then this will not impact your budget to heavily as they don't require food.
Is your reception safe for children to play? You would need to make all parents aware of things list stairs, water, roads, breakables and the like.
If you have a lot of children then you need to factor in their eating times - children need to eat often and earlier than us - can you make this work.
How do you think the parents would feel about you not inviting their children, would they have someone who could mind their children whilst they are at your wedding? Is your wedding close by so they could run home if needed? Consider each set of parents individually - see what your predictions are.
This should now be forming a pattern and be drawing up an accurate costing - does this help you make your decision?
If you are still incredibly torn then the only other suggestion I have is to speak to a parent that you feel will listen to your concerns and see what their opinion is.
The people who tend to ask are those who don't have children themselves - as you would expect. So the question from their perspective is more like "how do I tell people their children are not invited"
There is no set line that I would recommend using. I would suggest staying firm and not making exceptions - you both need to be on the same page with this. If you ever feel like giving in then it will impact your budget and also it could cause great upset on the day when some are there and others aren't.
A huge factor to remember is that its your money and it is incredibly expensive to get married these days.
Most people will also be hugely grateful to be a part of your special day so will be over the moon at the invitation. Plus - who knows, some parents may even be grateful of the day off to enjoy themselves.
I hope this is helpful to you - let me know how you get on firstname.lastname@example.org
Love Katie. x