How to get rid of crickets and large red ants without using pesticides

I don't use pesticides because it's just wrong for other living creatures, I have a 2 year old grandson and 2 springer spaniels that love to eat the grass.
The red ants have a black 3rd segment, no visible hill and have really long worn paths through our lawn. But they also tunnel underground if something is in the way. We have had a cricket problem since we moved here five years ago which is visible when you walk across the yard.
please help. Thank you, Donna Sulton

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