It sounds to me like you are running yourself ragged trying to meet the "neediness" expectations of your kids. My mom says either the adult runs the house or the kids do - kind of sounds like your situation is the latter. Perhaps there is some latent guilt regarding your situation? Are you trying to make up for Dad not being there and feeling like you owe it to them to give them the attention of a two parent household?
I watched my brother and his wife exhaust themselves with their first child trying to do this very thing. She wouldn't take naps, she would stay up late, they would get up several times a night because she would cry, she ended up in bed with them most nights - she ran the household. They were zombies most of the time just so exhausted. When my SIL got pregnant with their second child something had to change, so they decided THEY would run the household not my niece. In about a weeks time she was taking naps, stopped waking them up all night and no longer slept in their bed. It was a VERY tough week; however, everyone was happier and healthier. Same thing when they started her at school - she cried and screamed and they ended up picking her up. Then they stopped - niece adapted pretty quickly. When a child gets used to you running to them every time they want something oh boy, that's a bad place to be in.
There is nothing wrong with you needing your time you NEED it! There is also nothing wrong with children learning to entertain themselves and saying no to them sometimes when they want your attention. A regular sitter would be a great thing for you once or twice a week. If Dad is coming over on the weekends take advantage and LEAVE.