This topic has been discussed many times before... First question before you spend more money is there a market for what you would like to offer? Many parents get themselves a point and shoot camera and will probably will be happy with the results. Kids want inmediate satisfaction or digital downloads so they can post them in their favorite social networks. On the other hand, many organized leagues try to keep a slice of the photography revenue stream by giving exclusivity to one or two photographers for a percentage of their sales. This means that perhaps you will not gain access to the sporting venue to take pictures up close or on the sidelines.
I would rather try to go on with whatever equipment you have as this idea of becoming a sports photographer for kids can become expensive. If you are thinking football or baseball and would like to go full frame the you will not have the APS-C sensor and the same great lens you have now, will not be as splendid anymore as you will lose some reach. Then there is the issue if you are going to shoot only day games or also at night. The same camera you might get might not prove to so great at night. In any case, I was just thinking aloud...
I shoot with a 1DX and a 300 f/2.8 L II or a 70-200 f/2.8 L II and have a 7D as a backup.