I am also a single mom (my son is five). I've been divorced for three years, but had full responsibilty of my son since he was born (my ex never wanted him and tried to force an abortion).
I posted this response to another mom who had thw same question about getting their child to sleep in their own bed....
"I am a believer of tough love.
I am the parent and adult, therefore, my rules are the ones my son is expected to live by. If the rule is he sleeps in his own bed, then he sleeps in his own bed. The ONLY exceptions I make is if he is very sick, or if there is a thunderstorm (he is terrified of them).
My son also tried to avoid sleeping in his own bed when he was around 3. We went through the bedtime routine (bath, book, tucking him in), and then I turned off the light and left the room. I had a tall baby gate in the doorway so he could not leave the room and didn't keep many toys in his room. I simply left. He cried, he screamed, he yelled. I ignored him, and eventually he would tire himself out and go to bed. After the third night, he went to bed without the temper tantrums and after a week, I was able to take the gate down. He now happily goes to bed in his own bed every night and rarely gives me any grief over bedtime."
Remember to follow through on anything you say - positive or negative. I do the counting thing - "I'm going to count to three and if you don't quit screaming, you will sit on time out", or "I'm going to count to three and if you aren't in the bathroom for bathtime then you will sit in timeout - and take the bath afterwards anyway." When I get to three... I follow through and do whatever I said.
This applies to positives, too. "If you eat all of your peas you can have dessert". Okay, so there's still chicken and rice on his plate... but he ate the peas... so he gets dessert.
"If you get no time outs for three days, then we'll have dinner at McDonalds." If my son meets my requirement... then on the third day I'm choking down McDonalds (ick) while my son is happily chomping on McNuggets.
Children need consistency, so be sure to provide it.
Single parenting doesnt really get easier... but it does change and children go through phases... this phase will pass!