At this point of time, under the current circumstances, anurag thinking that cutie pie is with prerna is the best possible outcome because he has not separated mother and daughter. A situation where anurag had kep sneha hidden from the world and was meeting her secretly would've been disaster given that no one has the right to separate a new born child from her mother. Here, anurag is living thinking that his daughter is with her mother and he has given his daughter and prerna a better rlife away from the daily danger posed by komolika. He is the one who is living without both of them, and this was already shown through niveditas dialogue about how anurag used to wake up nights screaming for Prerna and sneha.
Questions like how could anurag be so careless, did he not bother to find out where prerna and sneha are, is frankly expecting too much logic from this show. 😆