But it is a LaCie NAS, not an Apple Time Capsule, right? They're rather different. Here's a Time Capsule:
See http://store.apple.com/us/product/MD032LL/A/time-capsule-2tb?fnode=4d for details.
From the image you posted earlier:
That's not what a Time Capsule's contents usually look like. Plus, there are three sparsebundles there, that look like they may be three separate sets of Time Machine backups -- one for ". . . MacBook Pro," and two for "Home Computer" (as if one is for an older computer with the same name).
A Time Capsule probably wouldn't be named "LaCie," and if there were multiple sparse bundles and/or other stuff, would all be inside a single folder, usually named "Data."
When you double-click one of those sparse bundles, that opens the disk image inside it. If it contains Time Machine backups, it will look like this, also from your first screenshot:
It sounds like "Home Computer" is your husbands's desktop Mac, right?
I'm assuming you're clicking the other sparse bundle, named for your MacBook Pro, to get that, correct? If there's any doubt, eject the disk image and double click your sparse bundle to be sure you have the right one.
Sorry to seem pedantic, but if we're talking about a LaCie NAS, not an Apple Time Capsule, you may not be able (or want) to erase it the way you can a Time Capsule.
I don't have a LaCie NAS, so don't know how you do things with it. It looks like all 3 sparse bundles, and your iTunes folder, and the MANUALS and SOFTWARE folders, are all in one partition or account or share (whatever LaCie calls them).
If you set each of those up separately, LaCie may have a way that you can erase or delete just the one with the MacBook Pro's backups.
If not, connect via Ethernet if possible, eject the "Time Machine Backups" disk image, and see if you can simply delete that sparse bundle via the Finder (that will probably take a very long time). If that works, then try a backup.