I think he should spend time just being with his daughter. For his sake as well as hers.
Two-year-olds can be hard work. But also they are such interesting little creatures, and have the capacity to really engage, particularly with a parent who is exclusively looking after.
It doesn't really matter where you go with a child this age. In the park, look at the grass, play with the mud, check out the leaves,the beetles, the birds. Or go to a museum and see what's there. Or a bus trip to nowhere special, get her to sing 'wheels on the bus'... Or read stories to her and act them out. Or, well, anything really. (One of my sons-in-law has his little daughter passing him his tools as he works on his motor-bike; she loves that; took him a while to train her, but well worth it; special 'together' time for them both.)
Yes, it can be tiring. Yes, you have to change shitty nappies and negotiate tantrums. That's all part of the deal too. I had a child who used to stamp both feet at once, as she screamed, "I wanted to ... ! I wanted ... !" (Fill in irrational childish desire.) But - take it from me - it's the good parts you'll remember when it's past. And it goes so fast ... and you don't get to go back and fill the gaps you missed first time round. (Though if you're really lucky you get to do it with grandkids later, too; that's another story well worth the telling.)
One happy memory of long ago; sleepy little girl clings to me as I try to manoeuvre the empty push-chair along; passer-by comments, "Oh, such love between you both". Yes indeed. Such love. That's what life is really about, if you get lucky.
(You can probably tell I'm a dad, not a mum. Go for it, you dads! You won't regret it; I certainly don't.)