T.A.
Hi there!
I too have a 3 and a 1 year old. (and also a 5 year old). My son did really well potty training, and I'll tell ya what worked for me.
I picked a time where I could just about completely stay home for 2 straight weeks. The first week, I left him naked to run around the house all day, or at least naked from the waist down. When he started to pee, he would notice immediately, and I would tell him to run run run for the potty!! The first couple days, he would run there, but it would be too late, but he would still try, and I would really praise him for trying. By the third day, he would just maybe start to pee, stop, then run for the potty, and finish up in there. By the end of the first week, he had figured out how to make himself go in the potty, and was getting the whole idea of it down. So, the second week, I only put him in underwear, and he got used to that. By the end of the 2 weeks, we were able to go anywhere with very few accidents, as long as we could go potty kind of frequently. That's it in a nutshell for him. It really did the trick. Oh, and since he would be so busy playing all the time, I also set an egg timer for 30 minutes, and every time it rang, I would excitedly tell him it was time to go try. If he went, then he went, and if he didn't, then he didn't. We just were happy as long as he tried. I think it is important in that 2 weeks too, that you don't go back to diapers or pullups for any reason whatsoever (except bedtime). Once you pull out the underwear, really stick with them the whole time.
Good luck to you!! I know potty training isn't the most fun thing in the world to do, especially with a baby running around.