I work full-time, but it is as 3 overnight shifts per week (2 on weekends plus every Wed night). I go into work in the evening and don't get home until the next morning, and typically I need to go the bed and catch up on my sleep. I am too tired, so there is no way I can play with DD for too long, if I do at all, so you are not the only one. When I get home, she is really happy to see me - I give her a great big hug and a kiss, tell her how much I love her, and ask if she's had fun with Daddy. My hubby is staying home for now and not working, so is in charge of taking care of 3 yo DD when I am either working or napping. It sounds like a crazy schedule but it still gives me more time at home than I would have otherwise.
For the days that I am home all day and have not worked the night before, I am available full-time for DD, and those are the times I am more of a SAHM. I will tell you that I do not play with DD for hours at a time. Honestly, it would drive me batty. Usually I got enough to do around the house (cleaning, laundry, etc.) because unfortunately DH (who IS the full-time stay at home parent) can't be bothered to do anything unless I ask him to (because he is still a man and does not realize what needs to get done unless I point it out). And I can only build so many block towers and build so many forts and make so many play-doh cookies. I do play with DD, but I also figure that's what toys are for - to allow them to play with themselves. DD loves it when I play with her and we have fun together but I also believe that kids need to learn to entertain themselves. My mom was a SAHM and I can't really remember her taking the time out of her busy day to play with me - she had enough to do and I was fine keeping myself entertained, it is what was expected.
I think a lot of moms feel guilty no matter what. Moms that work feel guilty for not being there for their kids but SAHMs feel guilty because they are home but maybe not constantly giving their kids their undivided attention. I think we all just need to stop beating ourselves up and realize we are doing the best we can for our families given our situations. There are plenty of ways you can give your kids the attention and one-on-one time that they need without necessarily "playing".