Removing Tile Behind The Cabinets & Linoleum Under Them?
Just bought a house and the kitchen had new cabinets, counters & appliances installed two years ago. Flooring was replaced too, but it’s some kind of cheap laminate nastiness that wasn’t installed well and needs to be replaced. We’ll have a pro floor installing buddy helping us, but much of the prep will be done ourselves.
Here are the issues
Cabinets were installed right over top of old tile so we need to remove that to install a new backsplash (most is behind cabinets, but some visible to right of ovens and at backsplash level). Any suggestions on how to do this? We’ve discussed taking off countertop, but we would also have to unhook in-counter gas stove.
Secondly, the flooring will be replaced by ceramic tile. We have a lose kick plate that allowed us to see that 1)thankfully, crappy floor isn’t under cabinets, but 2) old linoleum wasn’t take up so it IS under the cabinets. 
How should we deal with that? We may have to install new sub floor to accommodate the new tile
I’d prioritize the job. Figure out what exactly needs to be taken off, and in which order so you’re accomplishing the redo in the most efficient manner.
If you have to drop a hanging cabinet to chip off old tiling, don’t be afraid to do it. You can shim out the cabinet for spacing and cover any gap with quarter-round trim.
If you’re planning on replacing the countertop, it’ll be simpler to just unhook the stove and installing it back into the new countertop.
I’d spend some time at a tile specialist showroom and talk to their installers. It’s worth paying for an hour or so of their time to help figure out the best approach to your redo.
Good luck!
It may be more time consuming but I think your best bet would be to remove the cabinets and just get them out of your way. The gas cook top should have an easy detachable flexible hose joining it to your gas supply just make sure you shut off the gas first. For the old linoleum it may be very easy to come off if it is very old if not then you can use a hard steel scraper and hopefully that will work for you. If not you may have to put down new subflooring so you have a clean work surface for the tile rememberingtile needs to be completely level or it may crack. Consider using the hardi backer board
it looks like gyproc but is is meant for flooring applications you could possibly place this over the linoleum and then your tiles can go on top of this. If you got a professional floor installer he should know about this product.
Anyways as always just right to it the first time then to keep coming back to fix mistakes.
God Bless and happy renovating