Behaviour - Out of Character

[suedonym]

I have a female Maine Coon cat She is spayed and just lately, her behaviour has been out of character. A couple of weeks ago, she took to making her bed in the bathtub. About a week ago, I heard her yowling at a cat that was on the other side of the cat flap, obviously trying to get in. I suspect that this animal has already been in here. I opened a set of patio doors, and saw the cat run through the fence. However, he/it did not travel very far, and turned round and boldly looked back at me. He was too far away to spray with water. Since then, my cat has been highly agitated and has taken to living outside. She will come in when I call her, but is very cautious. She will eat, and then head straight for the cat flap. Yesterday, I managed to pick her up and carry er into my bedroom and stroke and groom her a little. She loves a cuddle, but her tail was twitching wildly, gradually, she started to relax and purr. She remained with me until I felt the need to go to sleep, and then she headed for the food, and out through the cat flap.

Usually, she is either on the bed when I wake in the morning, and will come up to greet me, or she is somewhere in the apartment, and will seek me out when she hears me moving around. That has stopped.

I spoke with the breeder the day previously, who suggested keeping her in, locking the flap and then placing something in front of it. I followed her suggestion, but Tallulah was beside herself, and frantic to get out. I had the box containing my drill in front of the cat flap, and she knocked it over in her attempts to get out. I stuck to my guns, and found her in the bathtub. She made a further attempt to get out, and I relented, and let her out, She was not here this morning, came back when I called her, ate and then headed straight out through the cat flap. I have just called her in for her snack, and same thing, eat and run.

There are two new cats in the area, one of them, I think is a Maine Coon cross who is very friendly. I do not think he is the problem. I believe the problem is with the other animal who seems to be highly aggressive, and worrying my cat. She obviously trusts me, but is uncomfortable in her own home.
I am considering spraying with one of those sprays that is supposed to get rid of odours, and am wondering if I should force the issue of keeping her i, which is highly distressing to us both.

Initially, I thought that her behaviour was attributable to the unseasonably warm weather, but I have revised my thinking, because all her signs point to a high degree of agitation.

Any suggestions would be very welcome.