I have ready your story and you are going throught the exact same thing I did. First of al I would not tell him not to come over and do the projects. What you might do is find something to do outside the house when he is there.
When he is with you and at the house doing things for you think about what he may or may not be telling the OW. It's likely he is not being straight with her and that certainly will not help in his building a life with OW.
Just a quick recap on my situation:
My husband moved out in January 2004. Married 19 years two boys one 16 and 9 at the time he moved out. I knew he was having an A but he didnt admit it until May 2004. H was doing the exact same thing, calling, emailing, coming over all those things. He didnt like being in the apt at all. At first I was ok with it and then after a few months I finally started getting a life of my own and doing things for myself. H didn't like that H moved back home in July 2004: unfortunately the A continued off and on until April 2006. He worked with the woman and it wasnt until a few months after he finally quit that it finally ended. It was a very long and very tiring road but like my situation, the A with your H and OW will come to an end. If you stay true to yourself and your children and what you have built with your H up until now is solid, then things can work out.
I still have my moments and sometimes I get so mad at him for creating this mess and leaving me with such bad memories and feelings to get over but he is back home and we are working together to rebuild and create new memories. OW still trys to contact H and cant understand why he doesnt want to stay in touch. I want so much to call her and tell her to get a life !!! but I don't because it will only stir up more bad feelings. Hang in there. Try to focus on you and the kids and not the OW. It is very hard and you will have you set backs but you will get to the other side.
