How can I tell if my parents have dementia?

I'm new to this forum and came across this via Google. I do not know where to go to get my parents help. My apologies for this being long, but it involves two people and I would appreciate any insight you can provide based on your experiences.

Both my parents are in their 70's. They recently sold their house to move closer to me and my family to be near their grandchildren and help us out. I've heard stories from my brother and some from my mother about my dad's behavior. Most of my life he was an unsavory character that would like to get to people's emotions just for kicks. Growing up he would embarrass us in public with weird questions and behaviors. This has continued, although it seems like my mom's new thing is that he's been cheating on her (well new as in the last 10 years). I'm not sure if any of it is true, but judging by some of her outrageous stories like middle-aged women climbing onto the roof of the house, I'm guessing it's not.  Still, that has not stopped her from getting a full on security system and making my dad a prisoner in his own home where she holds all the keys and even then she still accuses him.  She recently told me that he confessed to her about having an affair 15 years ago, but this is the first I am hearing of this so I'm not sure if it's true either.

When they sold their house and moved here, I naively thought that a new life with their grandkids would dissolve all of this, but two weeks into moving into their apartment my mom is accusing my dad of infidelity again. She always claims she finds things like grass on the floor or dog hairs in the car and they don't own a dog. Recently she said that she caught him red-handed an old woman that must of been in their bedroom and she came in and out of the window. Now again not sure if any of this is true, but I doubt an old woman would be limber enough to climb through a window, but maybe I'm wrong.

My dad's immediate reaction is to lose his temper to the point that he breaks furniture. It's gotten so bad in public that stores and places have had to question his behavior. They get into terrible fights to the point that the cops have showed up. Again, I thought this would stop once they moved, but I recently found out that the cops had to come to their apartment.

I'm at a loss. My mom accuses me of not believing her and I'm really tired of her and my dad's irrational behavior which is not limited to just losing his temper. I've caught him antagonizing my dog to the point my dog bit him and antagonizing my 4-year-old daughter to the point that she cries. I've also caught both of them lying to me in order to manipulate the stories to their advantage. I don't know what to do at this point. I'm not sure if they are exhibiting signs of dementia or what.

My mom also has a tendency to completely change the subject of a conversation we are having or redirecting it as if I was not talking at all. I'm not sure if that's a sign of dementia or hearing loss.  And my dad just acts strange. It's hard to explain, but he will will randomly spill things or hurt himself for no reason. He also brings weird things into our house. I've often found him passed out with a cigar on his lips about to fall on him and he's covered in cigar holes in his clothes.

I just want to get my parents the help they need, but I don't know where to start. They both deny anything is wrong with them. Sometimes I wonder if they are just gas lighting each other. I always feel like I am pitted between them and supposed to take sides. I would appreciate any help and or experiences you may have. Thank you for reading this.