Wife messages today saying "Daughter's birthday is in early August. Need to start planning in case you want to throw a party and invite people".
maybe something like "I have plans to take D xday-xday to celebrate, but if you would like to have dinner with us on her birthday, we can work something out"
Yeah that's along the lines of what I was going to suggest. Michele says it's OK to invite the WAS along in something that you are doing as long as it's clear you are going to do it whether she comes along or not. So it's taboo to invite her on a date, but OK to invite her ALONG for an activity. You mentioned dinner with D and W and that you are planning two days at a waterpark with your D without W. My attitude about stuff like this is let your W know, even if she's not invited. Because if you're taking D away for two days then it's just the polite thing to do to inform her since she's a coparent. So I would suggest saying something like: "I'm not throwing a party, have already made plans to take D to a waterpark for a couple of days. We were going to have a birthday dinner the night before we leave, you are welcome to join us for dinner if you would like."