Haven't tried it myself, but apparently you just lay down a new foundation tile, and snap new walls onto it.
Been having so much trouble with the game lately, too. First, Piper glitches out and won't travel with me anymore, even though her affection is maxed and I romanced her. Looking it up on the web, it seems this can happen when you don't finish an important quest conversation. Since I walked away from the Kellogg's Memory stuff(was doing Silver Shroud at the time), I decided to go do that. Then that quest bugged out. There were floating doors across the path, blocking you from finishing it. I tried finishing more quests, disabling any mods that added new objects, disabling all mods, nothing worked. Could not finish the quest. So I looked that up and it seems this is a known conflict with the Vault Tech Workshop DLC, which means Bethesda fucked it up. Fortunately, some one had a nice work around which wouldn't mean uninstalling DLC. There's a cheat mod called Spawn Items which lets you change player settings, including granting yourself 3 times jump height. That got me over the doors to finish the quest. (I also used the mod to set my weight limit to 100,000 lbs. Fuck you, encumbrance, I win!) So, I go back to Piper, still not fixed. Shit. So, I decide to go do Cait's quest. Ya know, the one that takes you to the very corner of the map? Well, every time I would get within spitting distance of the damn vault, a settlement on the other side of the map would come under attack. This happened like three or four times, even to Sanctuary. Ya know, the place with 230 defense from all the Heavy Laser Turrets I set up? Yeah. Ugh, fuck me.
Still, finally got that done, and I did get a mod that unintentionally fixed Piper. Basically, it changes her dialogue so that she stays flirty with you after you finish the romance side quest. It's actually really nice.
So, now I can send her to Red Rocket, fortify the place, ring it with Turrets and Sentry Bots with orders to shoot any man who approaches, and Piper can wear the red dress I bought her and stay pretty for me for when I'm done adventuring and need some "relaxation".