How to introduce a kitty to the outdoors?

My kitty, once recovered from her spaying, so a good week to two weeks, is going to have to be an outdoor kitty for a while till an apartment that allows kitties opens up, due to her staying with my Step Father (I still buy her food and stuff, but my husband and I are currently homeless till a place that allows cats opens up.)

Her grandfather -don't worry, he's fixed-, an experienced outdoors kitty, will be there with her, but I'm still worried. Is there a method to go about this? Or should I plead her case more to allow her to stay inside?

I already treat both cats with flea and tick preventive, ect and both fluffies have all their shots up to date.