I can see both sides here. You are effectively a single parent and have developed a way of coping with the day to day hard work of child rearing which works well for you and the children. He swans in occasionally, disregards all the rules and undermines your child rearing.
On the other hand, he is on the perimeter of his family and when he tries to reconnect by having fun with his children, you criticise the way he does it.
This is not an ideal way to live as a family and there are no easy answers. The best thing would be if he could stop being a frequently absent parent but I accept that if he is forces or similar, that's not possible.
So you need to have a very frank, open and hopefully non accusatory discussion where you both come up with lay some ideas for how to deal with this. You need to let him have some freedom to build relationships with his children without your interference. He needs to understand what a nightmare it is for you to cope on your own with children who think they can disregard household rules.
Decide on your most important household rules. I completely agree with no football in the living room. But maybe putting toys away before getting out more is not so important? Though, of course, it should not be left to you alone to tidy them away at the end of the day. Perhaps you can come up with a suggestion for how the house will be kept tidy that doesn't rely on you doing all the tidying e.g he takes on the responsibility for training the children to tidy up for themselves before he goes away again.