In south Alabama, my summer squash doesn't do well after the it gets hot (like now). I usually plant it as early in the spring as I can and it always peters out about this time of year. I'd love to know how to have it all summer too. I'll be watching this to see if anyone has the secret.
I don't think squash and potatoes would work planted together.

Plant Squash before really hot weather unless you're trying for fall crop then shading might be necessary they need plenty of water once it gets real hot Like NOW. I planted some potatoes in a tire. Lay the tire down prop open the middle fill it about half full of dirt put the potatoes around inside it and cover them, once the plants get up to the top add another tire and more dirt, I have read that you can go up to 4 tires high resulting in about 30-40 lbs of potatoes in a space the size of a tire.

I planted some squash really late, like June 15th or so. I just got a really late start in the garden. It is doing well, blooming a lot. But thus far no female blooms. The plant seems to be doing well though, is growing like a weed. I have high hopes of squash until first frost, we will see though.