37M and 40F - Upset over house chores

Hello! I am really struggling with a big aspect in our relationship, seems my partner (40F) does not feel I (37M) support her and the examples seem to be around the house.

Situation is she owns the house. Has a kid and a dog. We live in Puerto Rico. I travel away from the island often for work / family things.

I try to help out as much as I can, and always offer I am there if she needs anything, just ask. The problem is, she feels she shouldn't have to ask. Just kind of at a loss really on what to do:

• Offered to mow the lawn / weedwack. But she says she pays guys to do this.
• Offered to clean the house / laundry. But she says she pays a cleaner once a week to do this.
• Offered to take care of the pool. She says she pays a guy to do this.
• Started making breakfast for her and her son. She said she likes doing this. So I just clean up after.
• we can't agree on a dinner time, so I don't know when to cook.
• Offered to pay rent (of course), she can't sit down and tell me how much and says she doesn't want my money.

I do take out the trash. Pay the exterminator. And always pay for dinner when we go out / take her on trips and vacations. I have paid for a refrigerator in the past when it broke and bought a new one. Get groceries when I see we need them.

She constantly kicks me out of the house and ends the relationship. What's frustrating is it's over this. What else can I be doing? She is adamantly against asking me to do anything, having a chores list, or laying out how much money to be giving her. Whats the solution? Should I just send her money every month regardless?

TLDR: Live with my girlfriend, she wants me to do identify and do house projects in the house she owns and I'm not sure what to do?