I ended a text to my daughter the other night with Ich Liebe Dich. She has spent a lot of time in Germany and told me the phrase "Ich liebe dich" was used to convey romantic love, and it was better to say "ich habe lieb fur dich." Now I know Americans "love" everything from their babies to their bread, but the latter phrase seems paltry to express a mother's love for a child. Is there a better German phrase?
To add to HalvarF's answer and answer the 2nd part of your question
Now I know Americans "love" everything from their babies to their bread, but the latter phrase seems paltry
It's indeed much less common in Germany to say to love (or hate, for that matter) something than in US English. You'd pick a softer term to express that you like (or dislike) something, e.g., "ich mag keinen Spinat" (I don't like spinach) or "I mag das Lied gerne" (I like that song a lot).
If you want to express more than "hab Dich lieb" seems to convey, you can add an extra word as in "hab Dich ganz lieb" or "hab Dich ganz doll lieb".
The use of the German "ich liebe Dich" differs in fact from the use of the English "I love you". To a daughter or a son one would prefer to say "ich hab' Dich lieb" instead of "ich liebe Dich". The latter is normally used as a declaration of love in a partnership and sometimes it may even indicate sexual interest in a person.
Avoiding "ich liebe Dich" when speaking to a child is in a sense strange because most people say "ich liebe meine Tochter / meinen Sohn / meine Kinder" when speaking about them.
If you understand German and want to get a drastic example for an indadequate use of the verb "lieben", I recommend to have a look at this video (beginning at 00:38) from 1989 where Erich Mielke, the chief of the East German Ministry for State Security, says "Ich liebe – Ich liebe doch alle – alle Menschen – Na ich liebe doch – Ich setze mich doch dafür ein".
Well, in my mother-tongue speak which is North-Eastern German, the term "I love you" is indeed used chiefly in a romantic sense and it's a clear and straight statement, as straight as an arrow. The term "Ich hab dich lieb" is thus less straight, it's a softer and weaker term, better to be applied to one's children than to a marriage or living partner. But it's very much OK to say these terms to your dear ones, better often than never.
Grammatically, I concur with HalvarF's answer.
To provide a different perspective from a native speaker living in Germany about what would be usual to say, I'd argue even "Ich habe dich lieb." sounds way over the top. It would be appropriate in a romantic context again, or maybe among groups of (usually) younger girls.
The question is how
to express a mother's love for a child
in German. I think there is a very simple answer: You don't, at least not in an explicit declaration. It sounds extremely unnatural every time I hear it in a dubbed American TV show ("Why do they keep saying that?! They're parents and children, it's clear that they love each other!"), and as far as I can tell, declarations of the sort "I love/like you" to one's parents or children are something that is simply not done in German.
What is indeed somewhat usual is rather some sort of "praise" pointing out the special meaning of the addressee to the speaker:
Du bist die beste Mama der Welt!
(You are world's best mom!)
Du bist meine absolute Lieblingstochter!
(You are my absolutely favourite daughter.) (Use if you have only one daughter; this has the added benefit of being slightly humorous. In case of several children, you might want to pick a less exclusive wording such as "... elder/younger daughter!")
Depending on the situation/content of the preceding conversation, some more context-specific statements are also possible:
Ich freue mich auf euch!
(I'm looking forward to seeing you!) - if there's an upcoming encounter with the addressee.
Du warst mir eine riesige Hilfe!/Du hast mich gerettet!
(You've been a huge help for me!/You saved me!) - in case the addressee provided some help to you.
Hoffentlich können wir uns bald wiedersehen.
(I hope we will see each other again soon.) - to express you're missing the other person(s). Somehow, an explicit "Ich vermisse dich/euch." (I miss you.) sounds quite blunt to me.
P.S.: I'm on very good terms with my parents, and have always been.