You should receive two tags per person that is on your ressie. Once you check you bags in at the airport you will not have to worry about them in Orlando. Just go to the Magical Express check in with your carry ons, hop on the bus and go to the resort. Once you're at the resort if you can't check in they will store your carry ons and once your room is ready take it to your room. Very easy!! The only way we travel. I've never had a problem.
Not sure when the last time you used DME was, but they no longer send two yellow tags per person. It was quite awhile ago that they started sending only one tag per person. With the airlines charging more for a second checked bag, people weren't using that second tag, so they started only sending one/person. You are not supposed to cut those tags in half. Just peel the two small end pieces off to expose the sticky part on just the ends, loop them through your luggage strap and stick the ends together. The previous poster was correct though. You can just call them and they''ll send you extra tags. The toll free number is 1-866-599-0951. Also while it's true you can drop your carry ons off at bell services and they will store them for you, they do not deliver those automatically to your room (only the bags you checked). To get your carry ons you will have to either pick them up at bell service yourself or else call for them to be delivered. You would then be expected to tip bell services twice (one when you drop them off and then again when you get them back). The checked bags that are delivered to your room, Disney handles the tip for, but they don't tip bell service if you have to store the carry on bags.
I go to WDW several times a year and use DME every time. It's a great service and we've never had a problem. This past Dec I arrived at the resort, checked in, my room was ready, so I dropped off my carry on, and decided to walk around and take some pictures. By the time I walked around the resort (CSR) and was almost back to my room, I saw the cart that had my luggage on it. I waved the cart down, told him the bright green LL Bean duffel on the back of his cart was mine and I'd take it to save him having to run all the way over to my room. He told me he wasn't allowed to do that, that he was required to deliver it into the room, but for me to hop on and he'd drive me over there. He dropped the bag in the room and even though I know Disney handles the gratuities for drop off, I felt funny not handing him anything, so offered him a tip anyway. He refused to take it, saying Disney had already taken care of it. Normally after checking in, I take a bus to a park, and just find the bags in my room when I get back that night, so don't really know how long it takes to deliver luggage, but that day I decided to wander around the resort for a little while and was shocked at how quickly the bag was delivered. There have been alot of reports of it taking several hours to get your checked bags delivered though, so anything you need for the first day, you need to pack in your carry on.
I believe your little one should get a yellow luggage tag anyway. When you call to make the DME reservation (either by giving Disney or DME your flight information), they should include him. It doesn't have anything to do with whether or not he needs a park ticket. Even as a two year old, he is still listed on your room reservation. He's just under three and doesn't count toward the room occupancy and does not need a park ticket, but he's still on the ressie. To get on the bus, everyone must have a DME voucher. If you look in that DME pkt you received, a little over halfway through it, on a right hand side page you will see a page that has all of your names and a bar code on each name. That bar code is what they scan at the DME podium to get you on the bus and at that time they will ask you how many bags you checked and code it into a little hand held computer thingy. Mears gets paid according to how many people they transport on that bus. Your little one needs to be counted in order for them to get paid, so his name needs to be on that voucher page, where the bar codes are, so he should get his yellow luggage tag too. Call and make sure he is listed on your DME reservation. If I was you, I'd call the DME number direct, not Disney to make sure everything is correct.