Addict boyfriend... am I doing the right thing??

Hey ladies so to not make this too terribly long I ll give a little history first off... my soon to be ex boyfriend is a pain pill and heroin addict. Over our year and a half together I have had to see how these drugs damage those who use them. He has chronic pain which led to the use of pain pills in the start almost 4 years ago so I'm told. He made the choice to sell his oxy condone and smoke heroin instead, because ya know, he can't get over how easy and how much money one can truly make when doing so (😒).... I heard time and again how he will quit and blah blah blah... finally I had enough and basically gave him an ultimatum, he said he wanted to get clean. I took him to detox about two weeks ago and he was suppose to go to intensive outpatient and then inpatient by the end of this month. Anywho, for so so long I ve caught him in his lies and caught him red handed getting high in my bathrooms. I have two kids that are not his to think about and just started school again for nursing. I told him a couple months ago my biggest thing is trust in a relationship which he has so clearly broken... so he got out of detox last week and then lied about going to outpatient. He admitted on his own about lying... ok whatever... then I find paraphernalia two mornings ago and didn't tell him what I found and just simply asked him to be honest. His story changed like my 6 year girl changes her clothes in one day. So yesterday I asked him to leave. I am done. I know better. I love this man with all my heart and if he wasn't a drug addict he would fit my description of my perfect guy, so this is hard. Of course he is making me feel like I'm just giving up on him and throwing him to the curb and that he hasn't done anything wrong (when? Today?) But I am feeling extremely guilty nonetheless... I need to stick to my guns on this but I'm scared I'm not going to be able to follow thru... it took me 8 years to rid the guy before him who was extremely abusive but I finally did it. I know as I type this exactly what I need to do and how ridiculous I may sound. Guess I just need to hear that I'm doing the right thing for myself and my girls. Need some extra encouragement to stick with my choice. Thank you for reading if you did.