Wife does remote access to our office from that computer in the downstairs office. If I was to just replace that one with the iMac, could she still do that with the new Apple?
Is there anything the iMac can't do that the Dell can?
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While a mac can run windows, looking to replace the current Dell with the Mac in hopes of running your remote software may be pushing it a little.  It can certainly work but in essence you'd be running an operating system inside an operating system inside an operating system.  Performance would be questionable.  If you really wanted to do it, you'd need to purchase a copy of Windows and a virtualization software like Parallels or VMware fusion.  

Conversely, you could also do it on the Mac via boot camp and it would be no problem.  This would just require you to restart your machine each time you wanted to boot into either operating system.  So yes, it can be done but you may want to use Boot Camp instead of virtualization.  It really just depends on how much she's doing remotely.  What kind of tasks, how long, etc...