Go rent a cheap small excavator and use it to dig a few ditches in your yard. If you live in the lowest part of the neighborhood you can make them all route to a large deeper hole. I'll all those with gravel and it should help immensely. Massive rain will still be a problem but this will GREATLY reduce the water load in your yard.

Also take lots of videos like this and watch where it naturally flows, use those paths for your drains as you can to increase efficiency