homeowner woes and fur-mom concerns

It's been an insane few weeks in our household. We finally had our patio installed, although the process was certainly taxing.

It took longer than the 2 days that we were told, which wouldn't be a huge problem except that the workers never told us and just left, right before the 4th holiday, so they didn't return for two days. So, upon figuring out on our own that they were gone, we had to cancel our 4th plans last minute. On top of that, they left machinery and junk in the yard and two fence panels off the fence for the entire four days it took to install the patio. This problem was exacerbated by our new family edition:

Without fence panels and with materials in the yard, our fur-pup, Katniss, was unable to play in the yard and we had to put a hold on outside potty training. She then started using the carpet as her toilet. Once the guys left, and the house was again quiet, she returned to using the pee pads that she was previously trained on.

This brings me to our current state of things: we have an awesome dog who is cute, loving, and mostly listens, BUT doesn't understand that outside is the bathroom and she escapes from every device or room she is held in when my husband and I leave the house.
First, we bought a doggie gate and put it in the laundry room doorway. This is the room where her pee pad is, so we thought she could potty there and we put a doggie bed with toys within. What does she do? She learns to jump the fence.
We then go out to an event for the 4th and we put her back in the room, this time with an ottoman blocking the gate and four boxes on top of it to discourage jumping. What does she do? She jumps and bites on the lower box, pulling it toward her so the top box falls in her room and she can then jump the box and ottoman and escape.
Then, I order a play pen/crate. She came from a home that kept her crated a lot, so I didn't want to buy a cage crate. We left yesterday for 30 minutes. She tore through thick canvas to create a small, 5 inch rip and escaped.
Needless to say, yesterday I bought a cage crate. We practiced her going in the crate, praising her and even sitting there with the door closed. We then closed her in and went upstairs for about 5 minutes. Nothing but crying and trying to escape. I'm honestly not convinced this cage will detain her, but I'm more worried about her hurting herself trying to get out. She has intense separation anxiety--she was left alone a lot at her last home.

I'm definitely looking for some house training suggestions.