You can spend $1 on the gifts and show up for an hour, and spend the day relaxing, just don't stress about it and don't push yourself to do more. Make the gifts easy and simple, no need to run around everywhere and make it a big deal. There lots of cute little craft activities at the Dollar store or the dollar section in Michael's or Joannes. Or get a package of playdough, split it up and wrap an individual color in ribbon, one for each child. You can get cheap books at Half Price Books. You don't have to spend lots of money on fancy bags/wrapping paper/cards to accompany the gifts. Or, you can bake cookies and bring a plate of cookies as the gift. My kids favorite birthday gift, was a box of generic fruit snacks that was tied in ribbon! You can make slime, put it in a baggie. Make them 3 different colors with food coloring: http://chemistry.about.com/od/letsmakeslime/tp/slimerecip...
Or, you can regift some of the toys you child gets at his bday. I do this every year! My kids understand and don't care so long as they get to pick their favorite one to keep.
It's hard to get excited about things when you are overwhelmed, but it is also nice to be supportive, especially since she is also going through a very rough time. Remember, you chose to do the huge party despite your poor finances :) Is she attending your child's birthday?