No doubt at all -
definitely bring your own. Not sure who said
Disneyland's strollers are hard plastic, because they most certainly are NOT - they are green canvas. They offer NO support for an infant. They are fabulous strollers, but NOT for children who cannot sit up without support and assistance.
At only 2 mos, you want to be sure the stroller where your baby is will be clean, and your own will be. If you're flying, you'll need the carrier on the plane as well as in any vehicle you ride in to get from the airport to the hotel and to DL. And as others have mentioned, it will be a HUGE help in other places on your journey (airports, hotels, shopping, whatever else you have planned).
We have never once had our stroller disturbed while at the park (other than a CM moving it a bit during very busy times). That includes our parcels, etc. Not once = and we strollered it at DL every few weeks for 4 years. Now that DS is nearly 5, we rent (for free, thanks Disney Visa!) because we don't own one anymore. I have never ever once been concerned about our strollers at the park. Ever. Besides - your own will be much easier to find in the sea of green canvas strollers!
As for the changing stations . . . the Baby Care Centers are AWESOME! Each park has one. DL's is at the end of Main Street on the right side (when facing the Castle) right next to First Aid. DCA's is at the front left corner of the Mission Tortilla Factory in the Pacific Wharf area - also right next to First Aid. They are clean, the changing tables are huge and PADDED. The rooms are temperature controlled (heat/AC) so they're always comfortable, and they're big enough for more than one adult to go in. Extra nice with a squirmy baby . . . They also have stuff for sale (diapers, wipes, formula, jarred baby food, etc). It's not cheap, but a great relief when you really need it. They have private nursing rooms with rocking chairs, teensy toddler toilets, high chairs for less-chaotic feedings, and the most helpful staff ever. They even have rinse-sinks if you use cloth diapers (never ever seen those anywhere else in my whole life . . .) To this day I tell every adult with a diapered child about the BCCs.
If your babe needs a change before you can get to a BCC, then hit the closest restroom. ALL restrooms (as far as I know) have changing tables - MENS ROOMS INCLUDED, so Dad has no excuse.

They are a slab of countertop - no padding and no belts. Nice and big, but cold and hard. Not a problem, but just so you know. But they have large changing pads (thick paper towels) and a few rolls of toilet paper handy. Another option would be to use the main part of your stroller in full recline (if you do this, please do us all a favor and throw the dirty diaper in a trash can and not in the nearest bush . . .

).
I will say that the restrooms next to the Matterhorn labeled 'Princes' and 'Princesses' are not a good choice - they're the oldest ones in the park, and they're just too small to get the stroller in there easily. Luckily, the BCC is not far away from there, so I'd just keep heading to Main Street . . .
My goodness . . . yada yada yada . . . hope this helps!!
