I, Everything that you've written comes from the mlc script. Wanting to live in the house a couple of days a week, but doesn't want you to think that a reconcilation is down the road. It's not about your daughter at all, it's about what he wants and he doesn't want to inconvenience himself or his ow. I do think that there is still a connection with you and the house and that's one of the reasons he's wanting to stay there. He'll never admit it, but it's a sick way of being w/his child. He left, and yet, he wants to live under the same roof a few days each week.
As for the ow's vehicle, I understand where you are going, but you must put your child first. If this will give her time w/her father and a way to get out to other activities, there shouldn't be a problem, just as long as the ow isn't around her. Keep in mind, the more you try to stop him from inviolving the ow in your child's life, the more determined he will be to do so.
As for acknowledging the family events, you did well. You should them that you have nothing to be sorry for and it let's them know that you are not lowering yourself to the level of your h. However, please remember...blood is thicker than water and we do not know what he's told them. They do love to lie and make the story about us being mean, hateful, etc. for their excuse to leave.
Your h is in crisis and he's going about it the same way as many of them. That's why it's very important to drop the rope and continue on w/your life and do the best you can for you and your daughter. Take it one day at a time.
BTW, I do hope that you are feeling better.
Sit quietly, the answers will reveal themselves when you least expect them to. The past is gone, the present is a gift and you need to focus on today, allow the future to reveal itself when it is ready.