Congrats on a healthy baby first!
I would imagine returning to running/exercise is going to be dependent on the grade of the prolapse and if it continues to progress.
Do you know if it is a uterine or rectal prolapse, I am assuming uterine?
If it has not been broached, I would talk with your physio/OB about potentially getting a pessary no as a support for the prolapse. This will also potentially make your pelvic floor strengthening exercises more effective.
Additionally, I would avoid any valsalva - straining without blowing out your mouth at the same time. Increasing abdominal pressure over and over could (again potentially) increase the severity of the prolapse.
More things to think about: ensure that your pelvis is in proper alignment; work with your physio on overall regional exercises you can do safely that may help (low abdominal, lateral hips, etc); work on 'with baby' posture: think feeding postures, how you carry the little one, etc all to minimize stress on your body; I would go so far as to ask for the list of foods that is irritating to the bladder (i can get this to you if you can't get it) - I would work on the premise that you need to reduce as much stress and inflammation on your body and especially in your pelvis as possible. I mentioned to someone yesterday...park if you can near the cart return at a store - quickly grab a cart and put the baby carrier right in the cart instead of walking all the way to the store with it. Or alternatively, immediately into a stroller.
Without seeing you personally I think gentle low impact exercise: walking, pool stuff, appropriate resistance exercises, seated cycling (at a gym); if your physio hasn't done an internal exam to see what your musculature is doing when you are working on a 'kegel', I would highly encourage this. This information would inform what strengthening might be best for you.
Most of all, be kind to yourself! If you have the time, keep us posted!
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