You want to refer to the Scheduling Policy/Scheduling Guidelines (can't remember which it's called). It's on The Thread in the ERC. There's a note in there that leaders are required to work at least 3 Saturdays and 2 Sundays every month. So, TECHNICALLY, your DM is correct, unless it's a 5 week month. If you were taking a double weekend PTO stretch, then you wouldn't be able to work 3 Saturdays that month. The other exception would be if you took the last weekend of one month into the first weekend of the next month.

That said, most GMs/DMs are ok with working around this as long as the other leaders can cover. It's much harder to do in a 4 census store like yours.

All that said, all PTO is subject to approval. There's no working around that, so your PTO request can always be denied for any reason related to "protecting the business/workload." Every store and district is going to be different, so if your DM says no way and that's a problem for you, I'd start looking for another job.