I cannot help in relation to defending against spyware other than using a daily spyware scan. I could go into more detail on spyware scans, but it's obvious to me that spyware is not really the issue.
As DB Lady ( 2 thumbs up) said, the real issue here is trust, or a lack there of. Why would someone add spyware to there partner's computer in order to keep an eye on them? This type of activity and mistrust usually comes more from the self than from outside influences.
It is not for me to claim to know what your situation is, or what to do; however, I'm quite sure the computer 'thing' is a product of something deeper; having nothing to do with the use of spyware. I believe this kind of activity is a manifestation of a lack of trust for the self. One has to ask; why would this be?
That kind of activity is based on insecurity and fear. There is no trust in fear; that's a fact.
I can say that communication is the only means by which to solve this situation; however, trust is necessary for effective communication. And, trust in the self is imperative.
With Regards,
Daniel