How can we support his dad into letting us help when he says it's his responsibility?

I agree with the others. Do random acts of kindness - help him out that way, Bring some meals, cut the grass, etc. . Also look for an adult day care facility that can give dad a break.

I had my mom in a daycare facility that specialized in dementia care, they had various levels of care and support groups for spouses and caregivers. The experience was invaluable to me. My mom enjoyed going, she was entertained all day and had fun. Dad may also enjoy the break. Everyone may benefit from this type of scenario.

Have you tried phrasing your offer to your FIL as helping him because he is doing such a great job with Mom? I am a female caretaker of a male. The help I appreciate is when my sons come and do things that require tools. I don't know how to use tools for example. Perhaps there are things he is not familiar with that a female would know about - stuff like that. Most important let him know that he is in charge and doing a great job. Things like: Dad we love her too and helping with things would help us feel better. Another thought is: surely he would have a problem with buying her underwear and other female stuff. It sounds like you have a great family and are loving people. I wish you the best
ROSEPETAL

Please don't give up trying to help. It could be a matter of finding the right approach. My FIL was caring for my MIL, who had Alzheimer's. In the past, he had refused to acknowledge that Mom had a serious illness and refused help offered. None of us realized how difficult managing day to day household had become for him. He called me one day to ask me to change the bed because it was difficult for him, and I took that laundry home with me. That gave me an opportunity to offer to do their laundry each week - "while I was doing mine". In the process of going bathrooms to kitchen to bedroom to collect the laundry I realized that the house had become very unsanitary and I was afraid that they could get a staph infection which would be very very bad. I knew I had to talk to them about this. I talked to them first about my concern, then suggested someone I knew and trusted to clean the house every two weeks or so. They met the cleaning lady and agreed to have her in once a month to clean. I "spiffed up" the bathrooms and kitchen each week when I gathered the laundry, to keep things under control. They kept their independence and allowed my sister-in-law and I to do more to help them. Bringing meals over were presented as "sharing a new recipe." It worked out very well for all of us. I especially enjoyed spending special time with my MIL, daily, so that Dad could get a restful nap, knowing she was safe. She was still mobile, so I could take her out for mani-pedi treats and visited stores where she could ride in a non-motorized wheel chair with me chauffering. She couldn't remember my name anymore, but we had a lot of fun while Dad napped. I dearly loved my in-laws, and was only regretful that I didn't realize sooner how difficult things had become for them. Please don't stop trying to help.

Upon reflection, there are things you might do to help. Do the gardening, mow the lawn, see if meals on wheels can make a deliver, and/or just stock up the refrigerator with frozen meals he could microwave.

Hire someone to come in and sit with her so he can get out occasionally. Also, maybe a once a week housekeeper.

He is right. The "greatest generation" always "took care of their own". Tell him you can help in any way should HE want it. Otherwise, butt out, and of course his wife is getting worse. She has dementia, which is a terminal illness. When she gets to the point when he has to lift her for any reason, he probably will get help. It may not be yours, he may call professional help, or place her in a facility. This illness is hardest on men who are used to being cared for...

Do the grocery shopping, cleaning. Stay with her so he can get out.
Elders are very proud and don't want to give up their independence, plus your Dad is old school.
You could approach it as "Dad, we don't want you to get sick too"
This is what we want to do to help. It will take moving slowly.
Help with meals and laundry and general cleaning. Tell him it will give him more 1 on 1 time with his wife. More quality time.

What help do you think your FIL most needs?

And - there were also coupons for a movie with lunch - I'd take my mom and hubby would sit with my dad. Another trick was "I was just at Safeway doing my grocery shopping and they had milk at such I great price I swear I bought milk for everyone I know. I brought you some".

Sometimes you just gotta jump in - gentely. Things like bringing containers of homemade meals for the freezer - claiming you made too much and rather than throwing it away you thought he and MIL might like it. One year for Christmas I made my parents a "coupon book" that had chores in it - things like "Four hours of Housekeeping", "Two hours of Yardwork" etc. I had the first page list "Terms of Service" which listed things like "A weeks advanced notice" - this made it seem less like charity. The trick is to do it in a way that doesn't threaten his independence or his pride.