It sounds like your parents are insecure in social situations outside their home. Be patient, help them find their place in "your" life. Invite them over to your house and make them feel useful. Hey Mom, can you come over and watch the kids on Wednesday, I'll only be gone a couple hours. Hey Dad, we're barbecuing on Saturday, can you come early and get the grill started. Mom, will you bring that dish we love so much. Mom, I could use your help sewing these curtains, do you have the time to help me? Dad, the kids are struggling with reading, would you help them the way you helped me.

Personally, I like having my children over to my house. But they are so busy, I know its a burden. Turns out, they love coming over in the middle of the week for dinner. By mid-week they are exhausted from work and count on coming over to my house for dinner and not have to cook and do dishes. They get here at 6 and I make them leave by 8.

You are married, with kids now, and your parents are still stuck in parenthood. Help them make the transition, make them feel useful, help them find a new place in your life. They won't stop arguing with each other in their home - so accept it. If they start arguing in your home, simply tell them to wait until they are in their own home to argue.