Regardless of how you think your interactions with H went today, remember that OW won't be very happy when she finds out he spent the afternoon at your house. She will be imagining what happened there....and even if she didn't know today that H was there, it will come out in the future. It always does.
Is it possible that H wanted to be at your home just because he misses being there?
I agree with the idea that since H spent money from your joint account, you should be able to spend from the joint account too, for lawn service......or even better, to treat yourself to some pampering. Is there something that you REALLY enjoy and that would bring a smile to your face? Bright blonde highlights or a fake tan for the summer? How about bleaching your teeth at home (you can order whitening gel at dentist.net----I use DayWhite gel (don't swallow the gel))?.....Some bright red toenails? ........or maybe some bright peep-toe sandals?
After my H left I lost a fair amount of weight and had more time to take care of myself. One added benefit of this for me was that I noticed men looking at me when I was out running errands. Even though I wasn't in the market for a new relationship, it was a very nice ego-booster.
Be kind to yourself.....and pace yourself. This is a long journey. Slow and steady wins the race.