You have a noise issue. Spindle motors (well any motors really) generate a LOT of electrical noise when starting. Very often this will cause other nearby electronics to have problems. A VFD can compound problems as they are very often good noise production units as well. You need a line filter and/or line reactor depending on what type/size of VFD you have.
If you have a smaller 110V single phase VFD driving a 1 HP or smaller motor you can probably get by with a unit like this:
http://soigeneris.com/cncparts2.aspx. If you have a larger drive/motor or a three phase input drive you'll need to look at your drives documentation to see what they recommend. Most drive manufacturers will have reactors/filters available for their drives. A line filter like the one linked to above should be placed as close to the drive as possible. Depending on the size of the drive, type of power input etc, you may need a filter/reactor between the drive and motor as well. Take a look at your drives documentation to be sure.
The line filters I sell (above link) work very well but you just have to make sure that it will fit your situation. Feel free to send me a PM or email if you have any questions.