I had the same problem with my three years ago. Now I like to say I live in a gated community. I built gates for the doorways by attaching (with screws) 2 1"x3" wide boards to one door frame with hinges and putting 1" lath strips vertically. A hook on the other side holds it shut. When they chewed the wood, I attached an old wire oven shelf to it with plastic ties until they gave up.

Sort of an H with an extra cross bar. If you build one, you can make it as tall as you need, just add an extra cross bar if it's more than 4 feet tall.

I also used one on the cat room so the cats can get out but the dogs can't get in. Works great.

Mary