Children At Wedding Reception

My fiance and I are contemplating having no children at our reception. Most of our friends have 2-5 children each and with he and I being the only ones paying for the wedding it would be beyond our means to pay for all those children. Here`s the problem. My daughter who is 10 will be in the wedding. And I have one brother (who has 2 children) who is traveling clear across the country to walk me down the aisle. Is it appropriate to invite my daugther and my brother`s children only?