I had severe SPD and laboured naturally. I was not allowed in the pool as they felt I wasn't mobile enough to get out in an emergency. However each room had a deep bath so I got in that and did most of the labour there, and it helped a lot. I also used hypnobirthing for 3 days of the labour, and felt that this gave me a very positive experience, although i still needed pain relief in the last few hours. A warm hot water bottle between thighs/ lower back also helped when not in the water, but really the bath was a lifesaver.
If you have underlying hypermobility (hypermobile women are more likely to get SPD as the ligaments are already extremely lax) then you are at increased risk of tearing and also PPH as the connective tissues are weak. You should also be aware that local anaesthetics tend not to work as well in hypermobile women. If you just have SPD I don't think these are an issue.
You need to measure the maximum leg opening without pain, tie some string around it so you can use that a a guide in labour. You will need to brief your partner and MW very strongly about not opening legs beyond this, otherwise you may well make the SPD worse. In the extremes of labour or if you have an epidural or spinal you won't notice what's happening. If there's an emergency though I found that they just yank your legs apart and do what's needed, however many warnings they've had... This happened to me and my sister in emergency situations.
I have been told that women with SPD labour more quickly as everything's already loose, but can't say I noticed that with my 3 day labour, or with similar friends.
Recovery involved a couple of months still using crutches (for outside only), which was tricky with a newborn. Then another 2 years of pain and physio. But then I had severe SPD with underlying severe hypermobility. I kept bf for 9 months, and my physio said that would keep the SPD going longer.
For current pregnancy I am encouraged to have a C-sec due to severe tearing. The fact it would reduce my pregnancy length by up to 4 week and avoid a stirrups situation is something that I am factoring in to my decision.