Yes you'll get the MM entry every morning it's available - that's the key though, since MM is only offered on the days of the week specified regardless of which hotel property you stay in, and it does not matter if you are a DVC member or a regular non-member guest - it's not a daily occurance like at WDW where they mix it up between the 4 theme parks. As long as you are a resort guest staying in one of the resorts on any of the MM offered days you may use that benefit.
Did a CM confirm this to you? What you state above is the current offering for DLR guests. Given the wording on the site, it sounds like VGC members won't get this perk and would have to buy multi day tickets to get the 1 free morning like offsite guests. I can't imagine why they would do that, so we'd like to get clarification.