I keep a cornsnake and GCC in my home. The snake is kept in a tank on a shelf with the top blocked off by two metal screens an inch apart from each other. A sliding one and a locked one. I do this so Emmi's nails cannot reach the last screen and even though Lumi has never escaped, it's a precaution. Since Emmi has shown interest in watching the snake when he wakes up in the evening (Lumi sleeps all day under his bedding), I put a shiny deflated balloon hanging down from the top shelf so she won't try to fly to the tank and bother the snake. It's worked for two months. I don't see her fear of the balloon ending anytime soon, but if it does, the two screens will work and I can always switch to a blown up balloon! Haha! As it stands now, we walk by that balloon together and she flips out and flies away. Emmi is also never out of her cage when we are not home. If she did try to tear up the screen, she would not get far. I would hear it and her her making her "Wooooooooow Oooooh" sound. Lol She gives herself away every time when she finds something cool to her.
Lumi has a secured cage and always has, even before Emmi came to live with us. I'm so scared of Lumi getting out and getting somewhere we can't get to him. The couch with the recliner! How dangerous! The heating vents...certain death if he crawls in!

Thankfully he's never gotten out of his tank. It would take us not putting the tops on for him to get out. Hard to forget because we would trip over them! Lol A very easy simple reminder, cleaning them and putting them on a towel to dry in the walkway. Emmi also has a very secure cage and we have an extra clip too. Hard not to close the cage without opening the clip as its attached to the door. Another simple reminder.
I always wash hands and sometimes change clothes between touching Lumi or Emmi. It's second nature to me because I'm a preschool teacher. It's not possible for me to have both animals out at the same time either because I let Lumi climb out to see us and he won't before 9pm. Emmi is sleeping at that time anyways. I will never have them together because they would attack each other as they both are a preditor for each other. Emmi will always be caged when the snake happens to be out. I fear more for our little snake who never strikes his food if it's jiggled around and eats slow. Lol He also can't jump or fly to save his life and the only time he moves fast is away from live food! Too much work for him I guess. Lol Emmi however...I'm scared she would try to bite him out of curiosity.
Tanks work well for Rats. My rat loved his tank as it was big and I made a huge climbing gym and other cool things inside. Easy on their feet too. Who wants to step on wire all the time plus all that digging and tunneling in soft bedding is natural for them. Find a tall tank and have fun creating different climbing things and buy a reptile hammock. They love it! Plus with a wire top tank and balloon, your bird won't bother the rat. BIRDS EAT RATS TOO! How scary it might be to the rat to have your bird land on the top of your rat's cage? My rat used to shiver and shake when birds flew by the window.
Anyway, I hope I've given you some good ideas for securing cages and making a creative and fun environment for your rat. I think you will be fine keeping both animals in your home.

Honesty, I worry less about my two getting into something they should not be getting into then having a run in with each other. You sound like you are responsible enough to ask. You would not ask if you didn't care about having safe environments!
On a side note, I would not get a hamster ball for a rat. In my experience and from what I have read, they hate them and they pee in them and get covered in the pee as well as your floors. Have your kids build block mazes and other fun things. I bet the rat would love that much better!
My family: "Emmi" Green Cheek Conure (12/15/2012), One husband, two step kids, and one baby boy born in January 2015!