I have had all my pipes snaked and still water floods my bathroom when my washer is used. The pipes are four inches in diameter. The last plumber to come out told me I possibly need to change my toilet because mind is an older toilet. Would this be true and fix the problem?

You have two plumbers blowing smoke up your skirt. And here's why. You have a partial blockage downstream from your toilet and either plumber #1 didn't run out enough snake to reach the clog or he used a straight auger tip and the sludge simply closed up when he removed the snake. To loosen up the sludge he should have used a chain knocker or a drop head auger, (see image)
The second plumber was just plain stupid. There's no way replacing the toilet would solve your problem. Send that plumber back to Plumbing School 101. Toilets don't wear out! They can crack or break but they don't wear out period!
My advice? Call plumber #1 back and show him my post, Good luck, Tom