Laparoscopically will result in a much faster abdominal recovery, but won't make a difference regarding your butt healing.
I ended up having mine done open surgery and honestly the abdominal side of things was pretty straightforward even after having been cut wide open. It was the rear end side of things that really took a while.
As of today, I'm 4 months post-op, and back to full duties in a very physical line of work for the past 3 weeks.
So call it a pretty close to full heal in 3 months, doing everything I did prior....biggest concern was riding a bike, which I've already been doing, in moderation mind you, but I'm back in the saddle.
Hospital stay was 10 days I think, no lifting the kids for 8 weeks, and since then it's been a gradual progression back to normal.
Epsom salt baths really helped speed up my bum healing process, I encourage you to do this as soon as you're allowed!
So ultimately to answer your question, I'd say a good 3 weeks minimum of hands-on help from family.
It's a slow go at first, but you'll hit a curve and things will speed up. Build your team around you for best results, seriously. Do everything you can. Physio, chiro, counseling, naturopath, GP, ostomy nurse, dietician, and surgeon of course.
Any questions send me a message!!