Check out neighbors, friends, co-workers, the workplace (if they'll allow it), relatives or ANYONE with a monitor (maybe even an old one they no longer use) that will work with your video card to see if you can find one you can borrow long enough to do this.
I don't know both of your computers, but can you switch her video card as well as her monitor to your computer (you may need drivers but you can get them in advance and have them ready if needed)? If it's a separate card of a similar type that will fit in the motherboard slot, then this may work. If the card is built into the motherboard then forget it as it cannot be removed by anyone but a true professional. Just another option to consider.
The only other suggestion (not really a suggestion - more like an alternative that I don't really care for very much because I don't think it's a good thing to do but present it because it will probably work) I have is to buy a new monitor that works with your system. Make the required changes and confirm it works. Then you can decide whether you like the monitor enough to keep it or if it doesn't suit you (and maybe we sort of knew that from the start) return it for a full refund (confirm that's possible before you purchase it and how much time you have to do so). Save all the packing material and documentation and everything that came with it so if it is returned you won't be charged for anything being missing. It's a lot of hassle and maybe not exactly a nice thing to do if intentionally returning it is planned from the start, but it should resolve the problem (by which I mean, allow you to do your workaround).
Though to be honest, how you can live this way using her computer with remote desktop instead of actaully just replacing the monitor is beyond me. My wife and I would be at each other's throats to use what would really now be the one computer and there may be some things that cannot be done even with remote desktop (I don't have a list, but I've done it before with GoToMyPC and similar programs (never with only Vista's remote desktop) and in certains cases I needed the user to do some action that I wasn't allowed to do - and I imagine the same holds true here though I'm not completely certain - but I suspect you'll discover any such limitations if they exist in time. One likely limitation is the ability to make network changes - either by being denied access or because if you do you may not be able to connect at all (you may alter network access to prevent it from being possible at all) - remote desktop or mapped drives or anything - and then you'll be back in the same boat you started in only worse because you won't even have access to the mapped drives). While I cannot recommend this option unless you go into it actually considering that you will keep the monitor (in which case you don't really need remote desktop but you can enable it if you want just in case). Although it is a slight security risk to enable this feature, if your security is otherwise tight (you use an administrator account only when needed and a standard account most of the time, the Windows Firewall is enabled and exceptions are limited to only those you actually use, you have strong passwords on all user accounts, the guest account is disabled, and so forth) then it is a minor risk. I personally keep it disabled as I am a bit security-conscious but that decision is up to you. If it had been enabled, you wouldn't have needed to post here with this issue.
I hope this helps.
Good luck!
