I also agree with Mountainmanbob.
Its unfortunate, but as you stated you are "barely hanging on" to your job. Should you approach them about doing this you open yourself up to speculation and I hate it, but generally the first thing that an employer speculates is whether or not these issues will affect your job. I feel you will bring more scrutiny to yourself.
My former employer was very gracious about those enduring personal struggles to a point, and I watched that same person turn on people later. Skipping them over for promotion or special events as he speculated their issues might interfere with their performance. He grew not to trust them.
My advice would be to volunteer at a local shelter for the time being. There are other ways to help. When you have a solid year or two of good performance at the job with no issues then it may be the time to approach them about doing this.