So she loves him. He's loveable. You love him, don't you? I see that it unsettles you so note it. But deal with that in time -- its too new. Just FLAG it and ID it and let it be for now.
Longer prob is the time management.
I still do not understand why there is no schedule. It doesn't have to be "Fridays are my night, Saturdays are hers" type schedule.
It could be arranged as a pattern type.
"See me alone, then see her alone, then a rest day in our home no other people. Then everyone hang out together (us 3 at our house), then other family/friend things. Then a rest day. Start over."
So it can be loose enough to deal with the work things popping up. And the worst that happens is what? Extra rest days! Most adults sleep too little and need more rest anyway. Nobody will die. No 3 days in a row stuff without clearing it with you first since it seems to be a sore spot right now. Could be a "soft limit" that could change in time, but for now a limit. No "in a rows." Could they be more willing and able for that kind of schedule?
Could any of the tips in this help too?