I don't think you are being unreasonable at all OP. I feel just as you do. On the few occasions that my DP looks after dd he usually puts her in front of the computer watching nursery rhymes. I don't mind it for 5 or 10 mins, as she enjoys it, but like you, I don't want her just shoved in front on a tv/pc at such a young age (she is 20 months)....to me, now this is just personal opinion, but I think it's either a)lazy parenting (unless of course you've spent all day looking after them and just want 5 mins break), or b) total lack of confidence in looking after a child and don't know how to converse with them so instead the easy option is to put them in front of a screen and let that provide them with entertainment.
I do agree (and I do this myself) that perhaps as mothers we can often put our ideals onto the fathers and feel upset that they are not taking them out to the park in the fresh air or whatever, as to me, that is fun for the child, they laugh, crawl/run about (depending on their age!), and that in turn makes the parent happy as they can see how happy the child is. Who would want to miss out on that?
I don't think OP is suggesting that her DH takes their child out to expensive places....but fresh air outside costs nothing is good for kids and parents alike. I totally see that him just staying inside all of the time and seeming uninterested would be extremely annoying and yes, it does make you very resentful to have a partner who seems to not want to have quality time with the kids (I don't mean shoving them in front of the tv/reading the paper etc...that's not quality time).
Sorry, this is a bit close to home for me hence the rather ranty tone!! ha ha.
Like the others have said, I really would put off ttc with your DH with the situation as it is. If you feel like this with one child, he's not going to suddenly become Mr Hands On Dad with the second one. It is not a good sign that you can't bring your concerns up without him getting angry/sulking.(again, I know this from experience).
Perhaps say to youself that for a month you will just focus on the three of you having good quality fun family time at the weekend (forget about the separate time just for a month), and when you are in the park or wherever try and really get DH and DD involved, having fun together, and try not to interfere. Really try and be encouraging to both DD and DH and see if his confidence builds.
For the record, my soon to be ex DP also had a really crap father as a role model, like yours, so I wonder if they just learn these things.