It is not possible to "partition a partition." (Well, that's not entirely true; there are some exotic situations in which this can be done, but they don't apply in your case.) What you can do is to shrink the Windows partition and create a new partition for Ubuntu in its place.
As to dual- or triple-booting, you need some sort of boot manager for your Mac. Several programs can work, but each has its caveats:
- The Mac's firmware -- Holding down the Option key as you power on should bring up the Mac's built-in boot manager. Many users consider this a bit awkward, and the resulting boot manager is rather limited in its capabilities. (It might or might not correctly detect all your OSes, for instance.)
- rEFIt -- This boot manager is abandonware, but still usable for certain purposes. It has problems with Yosemite's LVM configuration unless you install it to the EFI System Partition (ESP), which requires manual installation.
- rEFInd -- This is a currently-maintained fork of rEFIt that better handles both Yosemite and Linux. Disclaimer: I maintain rEFInd.
- GRUB -- This is the default Ubuntu boot manager. It's not a good choice as your primary boot manager on Macs because it comes in two forms (BIOS and EFI), and neither type can cross-boot using the other method. Unfortunately, that's more-or-less required in a Windows/OS X dual-boot. GRUB is often used as a secondary boot program, though, in conjunction with one of the preceding ones.
There are other options, but the above four are the most common ones on Macs.
Also, you should be aware of the difference between a boot manager and a boot loader. The former presents a menu or command line that you use to select which OS to boot; the latter loads an OS kernel into memory and executes it. Some programs, such as GRUB, are both boot loaders and boot managers. The Linux kernel includes its own EFI boot loader, which also tends to blur the distinction, since this feature enables a boot manager to work a lot like a boot loader.
One more point: The way the Mac mixes EFI and BIOS-mode boots requires use of a hybrid MBR, which is an ugly and dangerous hack. Many users trip up on this detail, particularly when triple-booting, since many tools do a poor job of deciding which GPT partitions to replicate in the hybrid MBR, whose capacity is limited to at most three real partitions. You may need to use gdisk or the version of gptsync that comes with rEFInd (not the older version that comes with rEFIt) to create a working hybrid MBR for a triple-boot computer.
Overall, my recommendation is to not attempt a triple-boot on a Mac; it's too much hassle. Instead, install one or at most two OSes and run the rest in a virtual machine. That will be easier and safer to set up and will be less likely to cause problems. I realize this isn't always a practical course of action, but it's my recommendation whenever it is practical.
