"It is actually my mom."
Translation:Det är faktiskt min mamma.
Difference is: "Det är egentligen min mamma" would be used in a case like: "Oh look your aunt" - "That is actually my mom"
"Det är faktiskt min mamma" would be used in a case like: "That woman totally looks like you" - "That is actually my mom" So "faktiskt" can always be used when the actually can be replaced by "in fact"
I'll try to explain thisin an easy way but it is rather tricky since this distinction isn't made in English.
Sometimes, "it" would refer to a specific object. Then you would have to choose between den/det in Swedish as you say.
But sometimes "it" could refer to a general statement. "It" is more or less unknown, as in "it is raining" (det regnar). In a sentence like "it is a box" (det är en låda), "it" is also the general "it", since we have not really specified before what "it" is. But after this specification has been made, we would switch to "den" - "It is a box. It is red" (Det är en låda. Den är röd).
This is what happens in this sentence. "It" is a general "it", not a word exchanging "mamma". But here we wouldn't use "den" afterwards either since you wouldn't use den/det for people, you would use han/hon/hen.
So your two choices are
Det är min mamma. - "It is my mom" (det is a general "it")
Hon är min mamma. - "She is my mom" (hon is the pronoun which has replaced "mamma")