Should I be mad my husband won’t put my name on the house too?

Hi I’m a stay at home wife from 2014 till now but I recently got a part time job I really love. I also homeschool do the most of the cleaning and cooking. Usually when I leave to work dad is home. A week before we reconciled my husband got a house and told me to come home. So I did. While I’m here I do most of the child care cooking cleaning, and he wants me to decorate his home and at first I was all for it then I thought well my name isn’t even on this home. I could be doing renovations and upgrades to this house just to be left out or so he can move another woman into all my hard work. I’m actually really good at decorating and fixing up rooms and homes. The house isn’t the best looking on the inside and it has a roach issue in the kitchen. I come in clean up everything let him know what needs to be fixed. Just to be told that my name won’t be put on the home. Idk if I should care because I did leave him and I did choose to come back. I stopped alimony and child support payments because we reconciled in December. We also don’t have a prenup so if I was to get full divorced idk what I would be entitled too. Also he do keep getting caught doing weird stuff with coworkers and his girl best friend. I caught him bragging to her about this house and she sent him a racey pic. I sucked up my emotions and began to see what was going on got up got a job. So I can buy my own home when or if I’m ready to leave. I also don’t feel too bad about the house not having my name on it he claims it will be going to our son. Lowkey I felt betrayed and used because I was there forgiving him when he hooked up with his coworker all the sleepless nights and tears home cooked meals, trying to bring our family back together. Just to be treated like the fucking help. Then he says he doesn’t ask me to do anything I do but honestly things would pile up and get nasty in here without me. Please don’t judge yall. But do appreciate what you all have to say,