I wouldn't touch the dogs you could be bitten, as for the pictures or video just take them and keep them on your computer or whatever way you store them, make note of the date and time the picture was taken, I don't know how your area works, in my area our township doesn't have an animal control officer, so the duty falls to the County Sheriff's department to enforce our county's animal control ordinance. Where you are there will either be city, township, or county animal control ordinances, the county ordinance will be followed unless your specific town or city has it's own ordinance. I would start by calling the Sheriff's Department, I actually started by sending an email directly to my Sheriff explaining the problem, he gave my email to one of his Lieutenants who called me as I left my phone number on the email. He explained how they would handle the issue and that I was to make sure and leave my name when filing complaints against the dogs so I could be called on to testify in court and if possible to get pictures. The pictures can be given to the cops in the event they write a citation so they can be used as evidence if the dog owner goes to court to fight the citation. The Lieutenant also emailed me a full copy of our county's animal control ordinance, it covers everything from abuse and neglect to viscious animals and livestock protection. When you call or email the Sheriff's dept tell them where you live, give them your address and they will know whether they can handle your problem or they can direct you to the appropriate authorities be it animal control officers or city/village police department. It is too bad you are not from a gun owning household as many times the authorities are very slow to act on these issues, at least in my case they were/are. Taking physical action of some sort against the dogs is going to be the only answer if the authorities don't help you and they keep coming and harming your animals.
One other option is filing a lawsuit against the owner of the dogs, if they do damage to your animals you can sue for damages, also if they don't do damage but continue to come and harass and the authorities refuse to help, you can hire an attorney and seek an injunction against the dog owner, in this case the judge would make an order much like a restraining order where the court would be ordering the dog owner to keep their dogs away from your property and prevent them from running at large at all or they would face a consequence such as jail time or stiff fines or possibly surrendering the dogs. This is an expensive way to go as you need an attorney but if the authorities don't help and you cannot shoot the dogs this may be the only sure way to go.
You could also write an anonymous letter explaining that you are 14 years old and enjoy keeping your animals and inform the dog owner that their dogs have been coming and chasing and trying to kill your livestock on a regular basis and if it doesn't stop you will be forced to take action against her legally or otherwise. You may find that the dog owner has a heart for 14 yr old kids and their pets and will start locking up the dogs?
I see you are in Michigan and I believe I read a thread on here about Michigan having "right to farm" laws, those laws could very well have stipulations about being able to protect livestock from dogs, and they also may supercede any local laws which would contradict them.
