Neighbors cat!

Sophia • ♡ Wifey ♡ Boy mom ♡ Dog mom of 2 ♡

We had a new neighbor move in a few months ago and I guess she just got a new dog from the shelter and now she's decided make her indoor cat an outdoor cat. Normally I don't get involved however I am 8 months pregnant and deathly allergic to cats. Every time I open my front door her cat bolts inside my house. She's very sweet and for her sake my dogs don't mind cats but when I try to catch her she darts under my bed or furniture and being as big as I am I'm not fast enough to catch her so I have to wait for my husband to get home. My husband brought our neighbors cat back to her one evening and told her about my situation and how her cat keeps running into our house and she apologized and said she wouldn't let her cat outside again but the very next morning guess who's sitting at my door step waiting to run into my house again. Is there anything I can do to fix this? To make matters worse our neighbor only comes home maybe 3 days a week so the cat is left outside in freezing temperatures, no shelter or food or water. We live in a rural area so our animal control is almost non existent and doesn't really do anything.