How to boot from USB without re-installing the OS to the Mac hard drive

First see if you can boot you sister-in-law's iMac into Target Disk Mode without connecting to any other Mac. If it is successful, you'll see this on the screen,

you can follow the instructions in the link I provided previously to connect the two Macs, boot into Target Disk Mode and recover any files from the drive you need.

Since you don't want to reinstall the OS onto the internal drive, another option is to boot from the USB installer and install OS X onto another external HDD. Once done, you can boot the computer from that other external drive and then you may be able to navigate into the internal drive to locate and copy off the photos you hope to save.

You could also run diagnostics and utilities on the internal drive.

You can access Disk Utility when booted from the macOS USB installer.

Probably the easiest way forward is to install macOS to an external drive. Then boot from the external drive in order to attempt to access the data stored on the internal drive. You will need use Disk Utility to erase the external drive as GUID partition and MacOS Extended (Journaled) before selecting the "Install macOS El Capitan" option.

FYI, I would first check the health of the internal hard drive. More than likely the internal hard drive is either worn out or even failing. Trying to access data from a failing hard drive is tricky since the more you attempt to access the data the worse the drive failure becomes where even a professional data recovery service will be unable to recover any data. Most apps and even macOS itself are not designed to deal with the errors produced by a failing drive so they make matters worse. If you install macOS to an external drive, then you can use the third party app DriveDx (free trial period) to check the health of the internal hard drive. I can also provide instructions for checking the health of the drive by creating & using a bootable Linux USB stick if interested.

Also, the A1225 designation appears to reference 2007 to early-2009 iMacs so there is no Internet Recovery Mode. However, using Command + Option + R should allow you to access the local recovery partition to reinstall macOS without requiring authentication with an AppleID to confirm a previous "purchase" of the OS.

However, this is a very poorly documented option for the models without access to Internet Recovery Mode in their firmware. If you use Command + Option + R with them, then it will load from the local recovery mode partition, but not ask to authenticate with an AppleID to confirm a previous purchase of that currently installed OS. There used to be a vague reference to this in the official Apple documentation, but I believe this was later removed a few years ago. I think it was meant so when people sold their older Macs that the new owner would have a clean OS not associated with the previous owner's AppleID. Again, Apple was very vague on this.

A model too old for the Internet Recovery mode firmware will have shipped with a physical disk; there isn't a way to install 10.7 to 10.11 through the recovery system on them without it being tied to their Apple Account.

If someone installs 10.7 from one of Apple's thumbdrives, it won't create a recovery partition.

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From the Disk Utility, create a disk image of the folder containing the photos and store it on an external drive, or restore the whole drive to an external one.

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Depending on the OS on the iMac, restart with the Command and R keys held down or use an install DVD.

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Command + R loads the local recovery system, available on Macs with 10.7 or newer.

Option + Command + R and Shift + Option + Command + R load it from Apple's servers.

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