How do I allow my ex to re enter into the family?

Long story short. I was with a guy for 5years. We split nov2019 but stayed living together because he had nowhere to go. I out him out Jan 2020. We didn't split due to cheating it was more so fighting too much we both were slowly falling out of love an it hit a point where I was unhappy and tired of fighting. We JUST became corjal enough to sit and talk about everything we decided to work on the relationship. I have a 9yr old from a previous relationship and me and him have a 2yr old together. I'm very protective of my oldest and don't no how to go about it. A part of me does not want him to see my oldest becasue I don't want her to be confused as to us working it out and another part of me was wondering if I should allow him to see her and spend time with us (not living together) and get her back use to him. Right now he is living in a hotel and spending 4000 a month on that and living expenses. So I'm in question about if we should live together and be financially stable or continue to struggle seperetly. I may be over thinking it but I'm very cautious of the situations I have my kids in and I do not want to do something that can effect them later. I just need to no what seems to be the healthy way to bring my family back together. 

P.s. I've NEVER re dates someone I've split with so I've never had to go through the "working things out" process I have a low tolerence for cheating but with him it's more so our communication was horrible but that's fixable with work.