What to do is to go on your trip.

She's using classic emotional blackmail. Don't let her play you with it. The more you cave, the worse it gets. Boundaries are key. I've been there and it is very helpful to keep reminding yourself that YOU aren't doing anything wrong!!! But the emotional blackmailer will take any angle they have found to work on you to make you feel as if you are(!) They know your hot buttons. Oh yes indeed. Which is why it is so effective. But you need to see it for what it is: manipulation.

I went to Belfast 10 years ago and had a very nice time. Stayed at a hostel on Donegal Road. I was with my son (who was 13 at the time). We had a small but private room and it was very reasonable. It was just a short walk from the Botanic train station (we'd taken a train from Dublin). Aside from one tour, we went everywhere on foot. It's a very walkable city.

Use basic smarts like you would anywhere, like JustJenny said. If you like, you can use a measure of extra security against possible pickpocketing (I've never had any problem with that, but tourist areas can be prone to it), you can get a travel pouch that you wear under your clothes. You'd keep critical items like your passport and back up funds in it, so as to not risk getting stranded or having a big hassle should you become separated from your wallet for any reason. Anything you'd be wanting frequent access to (like some spending money) you'd carry in the usual way. No big deal.

Have fun!