Is it necessary to remove the engine to do a tune-up and are coils expensive?

No you do not have to remove the engine, but it may be necessary to remove the upper intake manifold. As far as cost, they can range from $122 to $283 list price depending on what engine you have and which bank the bad coil(s) is (are) on.

You do not have to remove the engine itself to do a major/ minor tune up. Some items on engine will have to be removed, such as air intake plenum in order to access spark plugs. Just as a suggestion.... Have this garage checked out for honesty/integrety issues with the BBB (Better Business Bureau). You can purchase coils on the internet cheaper than you can buy them at automotive stores. Hope this helps. Good luck.