Hmmm, yes, some of what you describe just sounds like he doesn't have experience with small children or any kind of parenting/child-minding skills - which is
More worrying though are the bits which sound like he just isn't that interested in relating to her. The part where you say he ignores her when she is trying to show hm something or talk to him - that is really worrying and a bit heartbreaking.
My own dad is like this with his grandchildren; in his case I think it is down partly to his age and the fact he's a bit deaf, but also to his attitude that kids should not interrupt adults - he's got a point, but he doesn't seem able to adjust his expectations for the kids' ages - I think it is fair to make a teenager wait for longer and not interrupt...it is fair to make an 8 year-old wait a couple of minutes...it is fair to make a 3-year-old wait by saying "hold on, granddad is talking; just one minute and you'll get your turn" - if you see what I mean! When he just ignores my 19-month DD because he is talking himself, I feel hurt for her and angry with him! I know that my dad was the same with us, and to be honest, it has had a lasting affect on me and my siblings and our relationship with him.
Your DP (partner) may not have very reasonable expectations of what a child that age needs or is capable of, and although this does not make him a bad person (again, it might just be inexperience!), I'd say he does need to change his approach or it will be very hard for your daughter.
A lot depends, too, on what the rest of your relationship is like. And how much he wants to be a connected family - or does he kind of begrudge your time with your daughter, her demands on finances and what you can do, etc...
I'd be concerned, because although 2 is a tough age in some ways, it is also rather difficult to 'dislike' a toddler to 'not get along' in the way that one can often (even easily!) dislike an older child. So it might get a lot worse as your daughter gets older, unless it is sorted out now. I have had at times to struggle with feeling "fed up" with my teenage stepkids, especially when they're acting up or being deliberately difficult - but I would have a tough time with a partner who felt as "fed up" with a toddler?
I would, if you can bear it, put the plans for a second child on hold until you feel more confident about this situation.