Yes, it is your place, so try to talk to him about this again.
I suggest you start by telling him that you have noticed that he misses a lot of what is going on (being said) if there are many people in a room, or background noise.
Mention the sound level of the TV and that it is too loud for the rest of the family, if it suits him.
Say it worries you to see him being and feeling left out.
Explain that hearing aids are so discreet these days that they are far less easy for others to spot than previously.
Offer to make an appointment for him, either with his G.P. or with a hearing clinic.
If he is still obstinate, then is the time to mention that you feel he is no longer really capable of looking after your children, as you are terrified by the thought that he might miss something really important that a child says to him.
If that doesn't work, then I am sadly afraid the only thing you can do is to make other arrangements for child-care and stick to them. Doing so might just bring home to him what he is missing.
My husband took upon himself the difficult task of telling my mother that she was no longer fit to drive. These tasks fall to our lot, as the child of elderly parents. They have to be done, but none of us enjoying having to do them.
Might your father be more willing to listen to your husband? My mother would listen neither to me, nor my sister, but she did listen to her son-in-law.