There are indeed connecting rooms at Little Mermaid, but I don't think ALL rooms have connecting doors. I'm not sure you'd be guaranteed a connecting door unless you had more kids in your party (think a party of 5 with three children over 10 so they can't all stay in one room). Since your kids can stay with you in one room, then if they're at or close to capacity (which at Xmas time is a distinct possibility), there might be a problem getting you a connecting room. But personally and anecdotally speaking, that's the sort of thing they try extremely hard to make happen. I'd suggest you call the resort directly, confirm that your request is in the system, and let them know there will be times your parents will need easy access to your room, so it's a big deal for you.
The one thing you should be aware of is that the rooms are very small, around 260 sq. ft (24.15 sq. meters). The beds are either 2 doubles or 1 king sized - I don't know if your 2 year old will be sleeping in a bed, but I'd almost suggest you our your spouse sleep in 1 bed with the 2 year old, especially if either of you is a bit on the large side. Those doubles can get cramped. Or if there's a chance of connecting king sized bed rooms, I'd think the three of you sharing a king sized bed would be more comfortable, and then your parents can have a king bed to share, too.
Because it's a densely populated resort during a very popular time, people might be kind of raucous, which is inconvenient when you have little ones who really need sleep and you might be trying to keep them on a schedule. I can't remember if the alarm clocks have a "white noise" option but I'd suggest you bring something to help drown out the outside noise a bit more. It might be tool cold for the pools which will help cut down on noise, but just in case, a white noise machine would probably help. But you could also always just use the radios in the room and dial to a frequency with no station, just static. We have a combination of lullabies with static in the background that plays and repeats all night.
Oh, and the food court. They have some tasty options, but it can be incredibly busy, even during slow periods, and it's cacophonous. If you either have a car of your own, or are budgeting for cabs or time-budgeting for Disney buses, I'd suggest trying to get breakfast reservations as often as possible, or planning on getting a grab-and-go breakfast in the park du jour. Trying to pick up breakfast for the 4 of us one morning in the food court and bringing it back to our room took 50 minutes, less than 10 of it walking to and from the food court/room. If reservations aren't possible, have a designated runner get to the court before it opens (I think 7am) and grab everything you need and bring it back to the room. Because the level of noise for 2 small kids who are already probably off their routine can make the beginning of the day pretty rough, to say nothing of how exhausted some of the grownups in the party might be.
I don't mean to be down on the resort, as it looks great and is impeccably themed. Just want you to be aware of these "cons" so you can plan ahead so they're not so "con-ny."