I never understood the idea that having mom (or dad) at home is the best thing for kids. When our daughter is at daycare, she's in a very stimulating environment staffed by energetic 22-year olds on 6 hour shifts. When she's at home with me my instinct is to bribe her with some ice cream and park her in front of her iPad. My wife has slightly more desire to engage with the kid, but no more energy for it--she's pretty…
When I'm home with my three kids, my instinct is to think of the skills that will aid them later in life and work on that through various levels of play. Often that's sports - practicing basketball, baseball or whatever sport they happen to be doing at the time. Other times that's academics where if I know they're having a problem with sight words or multiplication I will work on that with them. Sometimes it's just playing video games together.
Looking back on being a father I think to the things that they do on a daily basis and remember, "My wife and I taught them to do that." All the time spent working with them on crawling, walking, talking and everything since then has created fantastic memories I wouldn't trade for anything.