I have a 2015 MacBook Pro with a MagSafe 2 charging cable. My wife has a new MacBook Pro from 2016 with USB-C. I was wondering whether I could technically (in the matter of electronic feasability) use her charging cable on my MacBook and vice versa with some sort of adapter / dongle, and, if so, where I would get one?
You don't want to mix those two.
Because the USB-C port conforms to the USB 3.1 Power Delivery Specification whereas the Magsafe charger does not. Part of that specification includes the negotiation of delivered power. The Magsafe will not negotiate how much power is supplied. What it's looking for is the presence of the 1 wire charging circuit before it begins charging.
There may be adapters/converters on the market that will convert one interface to the other and vice versa, but (IMO) those cheap adapters are not worth the risk of sending the wrong voltage to your very expensive MacBook Pro.
Bottom line, use the genuine adapters built and designed for your MacBook Pro.
The ElecJet Anywatt One fills this need, for the purpose of powering a USB-C device from a MagSafe power supply.
From the product page:
Anywatt built-in self-developed LDR6032 smart chip supports the latest USB C Power Delivery & PPS protocol, Automatically recognize the end device needed power and adapt the voltage and current to best suit the end device charging purpose, range from 5V@3A 9V@3A 12V@3A 15V@3A 20V@2.25A and PPS 3-12V@3A MAX.
It is not licensed by Apple. That said, I own one and have been using it without incident to connect my 2016 MacBook Pro (87W) to my Thunderbolt Display; it can't provide the full 87W, so the battery charges somewhat more slowly than it would if I had the big charger with me, but it's been fully adequate in practice.
You can buy adapters (dongle) that converts USC-C PD signals to Magsafe1 and 2 (and in fact to any needed voltage to any old laptop). There also the inverse adapters that converts from a Magsafe 1 or 2 chargers to USB-C output to charge a modern computer although less useful.
The irrational claims of how a computer or a charger could be fried is just a old wives fable. You cannot over draw current for a USB-C PD charger because it will shut down. The charger cannot provide more than its design capacity nor provide more current than the load needs!
The reverse of charger providing "too much" of something or another that could fry a computer is also untrue. No computer use the direct charger input for operating the computer or charging the battery. The voltage is regulated by a DC-DC converter to generate the needed voltages. If the provided voltage too low, it will not charger; if the voltage is too high, the charging circuit will shut down.
Electrically, it is possible to go from either direction, it just requires a computer (microprocessor, etc) in between to do the USB-C PD negotiation. As people have noted, there are plenty of MagSafe2 → USB-C PD options.
There are only 3 wattages for MagSafe2 chargers and they have well known voltage / currents. The MacBook knows what the max wattage for the charger is by getting the id of the charger from the MagSafe2 plug itself. It won't draw more current than the charger will allow because it knows which charger is plugged in. Any USB-C → MagSafe2 dongle would essentially ensure the wattage via USB is available and emulate the correct MagSafe2 charger ID.
There does not seem to be a USB-C PD → MagSafe2 option, possibly because it would require a charger that supports enough wattage to both power the MacBook (45W/65W/80W) and the dongle itself. So at a minimum, ~50W to supply 45W (which is only enough for a MBAir and not enough for a Pro).
As others have said, the standards being different makes this kind of dangerous if you're not careful what you're buying.
But if you only want the magnetic connector (so that it doesn't pull the laptop with it when tripped and such, you could try one of these options to convert the USB-C connector to a magnetic one.