I approached potty training COMPLETELY differently than anyone else in the universe.
I said NOTHING about it. Except that she saw me go on the potty and one day she asked and I said "big girls go in the potty. one day you'll go in the potty too".
One day when I picked her up from day care she said "Gabby has princess undie pants". I said "yep. Gabby's a big girl and goes in the potty. Not in her diaper. when you are ready to go in the potty and not go in your diaper anymore you tell me and we'll go get you whatever kind of undie pants you want". We had this conversation probably 4 times over about a 3 week period.
One day she said she was ready to have princess undie pants. She was a few months older than 2 1/2.
We got princess undie pants.
I asked her if she was sure, cuz we weren't going to have diapers and undie pants and so if she had an accident it would be messy and she would have to clean up and try again. She said she wanted to wear princess undie pants.
We THREW AWAY every diaper in the house.
She had a couple accidents scattered through the next couple days. There was no reprimand. No heavy sigh. Just "That's ok. let's change and clean this up. You'll do better next time". I made sure I didn't go anywhere with her that would take too long for about a week.
You can do potty training a couple ways. I chose to do it the easy way. When SHE was ready, could communicate with me and understood that the "reward" was she was a big girl who could master that skill AND have big girl undie pants. And that the 'consequence' was she just cleaned up her mess and tried harder the next day.
You can do all that other stuff if you want. reward charts and m&ms and punishments and crying and power struggle and it takes months and months. It's up to you. You can potty train yourself by putting them on the potty on a schedule. OR you can let them really understand and own the process.
Personally, I wouldn't potty train them at the same time. They aren't the same kid. Potty training is a PHYSICAL DEVELOPMENT MILESTONE. It's also an EMOTIONAL DEVELOPMENT MILESTONE. Why would you expect your 2 kids to meet that milestone at the same time if they are different ages. Did they walk together? Talk together? No. I'm actually surprised your ped suggested that.
Whatever you choose, good luck!
Oh - ETA: I never ever used a different or special potty. What happens when you are out somewhere? Will you take that potty with you? But, I had a girl, so she could just sit on the edge of the seat and it was OK. I don't know how it works with boys!