I can see why you are pizzed!! But, in the scheme of things, it is probably best to choose a different date yourselves, and avoid the problems. Sounds like you are getting into an interesting in-law situation!
How far apart? I married a month apart from my cousin. We were not close, so the family didn't get uptight about it. I would say one and better two moths apart. More if any of the bridesmaids will be the same. It is usually the poor bridesmaids who take the biggest hits, two gowns, shoes, gifts, showers, it is a lot to ask to do it a month apart.
You guys could still get married yourselves privately and have a recption later, I know that is a dreaded thought for a first time bride, so I don't blame you if you think that ideas sucks.
All I can say is, try to go w the flow. Weddings are soooooo stressful as it is, it is waaaaay toooo soon to let yourself already get upset. If something is causing you stress, change it so it works for you. If you still want to get married in May, do it, pick the first weekend!
But sometimes it is just not worth the stress and hassle when you are dealing w unreasonale people. October is a gorgeous time to get married!!
(I'll whisper this, b/c you'll probany throw tomatoes, but anyway you can do a double wedding? Weddings are soooooo expensive, it would really save you a bundle! More for your new home or honeymoon!)