They would get to my home the same way i get to theirs. Bus and train. Im starting to wonder if youre being a bit biased in some of the replies. Inconvenience on mom? Shed travel after work JUST like i travel after work. Everything would actually be equal if we did it that way. Im actually making things convenient for her currently by her not having to travel at all considering its me thats doing it... After work mind you.
To be quite candid, I am a little biased against you, but only because you are insisting on talking to your girlfriend while in mom's home. I would be equally biased against mom if she were talking to her boyfriend while in your home.
Plus, I think that your current arrangement is a wonderful one for the children, they get to see both of their parents nearly every day and THEY do not have to travel to do so. I think that you are on the verge of messing up a great thing for your children, just because you cannot be respectful enough not to talk to your girlfriend during the few hours a day you are in mom's home.
My ex and I had a somewhat similar arrangement to yours when our daughter was small, and he would have never dreamed of talking to his new girlfriend while he was in my home. He would have considered that to be horribly bad manners.