Time to set a boundary op. Boundary setting btw is about what is acceptable to you and no one else.
Did your dp tell you about his dad moving in after it had happened op? Or did he consult? And was this before or after you’d agreed to move in? Or has the dad imposed this on his son?
^^ The answers to these qs will tell you a lot. Always look at people’s actions in addition to their words.
Perhaps a different way of dealing with this situation would be for your dp to have his Dad to stay in his house as long as he wants.
And for you to say to your partner “I understand about you wanting your dad living with you, but now circumstances have changed, I think it’s best for me and my child to rethink moving in with you” and mean it. Note that I said “rethink” and not “delay”.
I know this probably isn’t what you want but you have to set a clear line.
If he didn’t bother to consult with you then you are perfectly entitled to make unilateral decisions too.
Another alternative is to delay the move and get to know his dad and see how you and your dc get on before moving in, if you can contemplate doing that, over a longer period of time. If you form a serious relationship with someone, you are bound to encounter their family at some point.
Fair enough though if that is not what you had envisaged and you need to be clear that you have as many choices in this situation as your dp. It’s not all about him making the decisions.