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Since I got a few smaller mirrorless cameras I do use my DSLR less but it still gets use when I'm really planning on taking pictures when out and about.
As well as the Olympus I'd also look at the Sony mirrorless efforts. They're still much more compact than a normal DSLR but a bigger sensor than the m4/3 (same size sensor as the 60D). They're good as a point and shoot but do have all of the extra settings for manual shooting.
Or look at something like the RX100 (I'd say version 3 with the EVF) if you want something that really isn't a DSLR but still takes better than mobile pictures.
My current setup is a Canon 60D with EF-S 17-55mm f/2.8 and EF 50mm f/1.8 lenses. We've got a kid incoming any day now and my wife is a bit intimidated by the camera but is cautious about spending cash another one. I'm considering the Olympus OM-D E-M10 Mark III as an option suitable for both of us. It's currently £430 with the 14-44mm zoom which is affordable. I think that will suit her much more and be handy for me when I don't want a big camera about my person.
I originally bought the Canon to shoot my work (graphic designer, shooting print work mostly). My brother had the 60D and recommended it for remote shooting hooked up to my computer, which it does really well. I got it for £300 with just over 1k on the shutter count. I was just using the prime lens my brother gave me to shoot books but decided on investing in the 17-55 lens so I could actually get use of the camera outside of the studio, which I do, but my wife hasn't taken to it at all. She's a bit of an introvert and I think she feels a bit self conscious with a DSLR sized camera and relatively big lens.
Does getting the OM sound wise? Or will I just end up always using it in which case I should sell what I've got and could then get a couple extra lenses for the OM second hand and have all bases covered? If I can successfully shoot my work with the OM I'm wondering if the 60D would ever get used again?