I was wondering if it were possible to double register my horse. Her father is a registered Quarter Horse and her mother is registered Paint. The only problem that I can see here is that the sire was crossed with a TB. I was half-hoping I'd be able to double register her regardless.
If it the April Rain horse in your album, she most certainly qualifies for Pinto papers. They will only cost about $60 with the membership.
As for AQHA, she would need to have parents that are eligible for registration under the crop-out rule. All ancestors would need to be AQHA registered before she could be. The fees for horses older than 4 years are $1000 each. Unless your horse is a serious show competitor or breeding animal, it wouldn't be worth the paperwork hassle and costs.