She has no right to enter the property to trim a tree in your yard, and she does not have a solar easement.
Small claims court can issue an injunction against her trespassing, and can award nominal damages
for past trespassing plus any damages for harm to the tree.
If she won't mediate, it sounds like maybe a Judge needs to order her to stay out of your property. I assume the police may have told you "this is a civil matter" already, so small claims court may be your best option.http://www.dca.ca.gov/publications/small_claims/index.shtml
explains how to use the small claims court. See alsohttp://www.courts.ca.gov/selfhelp-smallclaims.htm
Another option would be to have a local attorney send a letter warning that any future trespass will result in legal action. You can get a free consultation from some of the local real estate
lawyers listed athttp://lawyers.findlaw.com/lawyer/firm/Real-Estate-Law/Berkeley/California
The structure might be in violation of the setback requirements of the local ordinance:
23D.08.030 Setback Requirements for Accessory Building or Structures
D. No accessory building or enclosed accessory structure that is within 75 feet of the front lot line may be erected or expanded so as to encroach closer than four feet to the side lot line, when abutting another lot. Any such building or structure which is located in excess of 75 feet from the front lot line such a building or structure may encroach closer than four feet to the side lot line subject to the fire isolation requirements, including setbacks and/or fire resistance wall requirements, of the Berkeley Building Code.
If this structure is within 75' of the street, you might want to call Code Enforcement and see if it will order her to remove it from touching the fenced property line, see
their page athttp://www.ci.berkeley.ca.us/ContentDisplay.aspx?id=6192
You can schedule an inspection throughhttp://www.ci.berkeley.ca.us/ContentDisplay.aspx?id=636
I hope this information is helpful.