Since no-one else has replied to this, I'll have a crack...
I'm going to ignore all the idiotic things like not having the quick release fully unwound, or having a tyre that is too fat to clear the seat tube or the brake calipers. I have seen idiots try these things often enough though.
No information has been given about the number of gears on the various wheelsets used. Might be worth providing that information.
If you are using a rear hub with an OLD of 126mm then it's made for a freewheel running 6 gears or fewer. If the freewheel is a more modern 7-speed or 8-speed version, then the width of the cluster is probably your culprit. It could be striking the chainstay, which would prevent the axle engaging with the dopout. I suspect this because your bike sounds like a racing bike with tight clearances, and the short dropouts mean the chainstays are actually very close to the freewheel, especially if you are using big sprockets.
Have a look at the rear axle on the drive side, and make sure the outer locknut protrudes a good couple of mm past the outer sprocket on the cluster. If there is sufficient clearance, then you should be able to spread the rear of the frame to slot the wheel in. You should then be able to see if anything is touching as you spin the wheel. Naturally, if there is a granny cluster with a 15-tooth small sprocket you are much more likely to get interferance with the chainstay than with a 12 tooth sprocket.
If you are struggling with anything I have said here, I would suggest just unscrewing the cluster and the Mavic wheel should just pop straight in.