How else can I approach the asking to go home?

Thanks to everyone for your answer. I will try these suggestions...

Try varying the fiblet...there is a broken pipe, we need to wait for it to be fixed... The roofers are there, in a couple days...
Follow that up with something enticing...let's have ice cream.

I read one husband who said he would take his wife for a short drive and when they got back home, she was happier. My mom liked to take a drive as well.

I have my mom and mother in law too but my mother in law is of sound mind. You do deserve diamonds in your tiara ;-)

I think you got some good suggestions above. I usually say do what works and try a few things. Normally, based on my experience, there isn't any anything that will solve this kind of issue. They may continue with the behavior or it may phase out. It did eventually stop with my LO, but, she changed over and starting crying out for her mommy and daddy, which is more heartbreaking. She seems to really be on a toddler's level now, but, medication did seem to help her be more content. You might explore that if you feel that she is becoming too agitated or suffering mentally during these times.

And, I might explore additional help during these times, if funds are available.  If someone else could come in and read, play music or distract them with some sort of activity or treats, it might be worth a try. 

I used medication and "fibblits" while my mom was in rehab. She is mid stage dementia. I used: when you get stronger
When the Dr. says you can
Want to go for a spin in the wheelchair? Or a walk?
Redirect, distract, change the subject. I know this seems to go on forever some days. You don't deserve a star in your crown.....you deserve a flipping row of diamonds for taking care of two of them! Bless you!

Google "sundowning". Many dementia patients become agitated in the afternoon, no one seems to know why.

Definitely talk to your mom and MIL's doctors about this as a symptom. Agitation sure must be unpleasant for them, and they deserve relief if it can be gotten from some medication.

Marty, please note with Alzheimer's/Dementia [as per your profile] when a patient says they want to go home, usually "home" means their childhood home, back when life was so much simpler and fun. And in some cases "home" could mean going to the Lord.

It took me a while to realize that my own Mom [98] was referring to her childhood home instead of the house that my parents had shared. Once Mom asked to visit her sisters and her parents, then I knew.

My you have your hands full, even with the help of a caregiver during the day, having both Mom's in your home. My Mom was in a skilled nursing facility as she needed a higher level of care. My Mom thought she was staying at a motel :)

As for the therapeutic fibs, I used as many as I could to appease Mom about going home. I was lucky, she accepted each and every one, mainly because a few minutes later she forgot about going home.

As for Mom trying to get out the exterior doors. I read somewhere that placing a black throw rug in front of the door might help. To someone with dementia, the black rug looks like a hole in the floor so they won't step there.