Translation:You will learn to love your baby.
Indeed if you just have "Je zult leren van" it means "You will learn from" "Houden van" means "to love" So they both use the same preposition.
I think i would use a passive to translate your sentence: "Je baby zal je leren lief te hebben." Or "Je baby zal je leren te houden van XXX(you need an object here)."
'van' is part of the verb 'to love'. To love = houden van. You really need the 'van' part, otherwise the sentence has a different meaning. Some examples:
ik hou/houd van de kat = I love the cat
jij houdt niet van hem = You don't love him
jij houdt de kat = you keep the cat
jij houdt hem = you keep him/it
Houden itself means 'to keep', but you can add a lot of prepositions to it ('van' is one of them) and then the meaning changes. Other examples:
hij houdt van zijn hond = he loves his dog
hij houdt zijn hond vast = he holds his dog
hij houdt zijn mond dicht = he keeps his mouth closed
hou ermee op! = stop that!
ik kan het niet bijhouden = I can't keep up
om te (doen) translates as "to" in the sense of producing an effect or achieving a purpose. In English, you can also add "in order" to emphasize this:
Ik studeer met Duolingo om Nederlands beter te spreken. - "I study with Duolingo [in order] to speak Dutch better."
But when you are just using non-auxiliary helper verb (like "learn to do" or "plan to see) then you just use te (doen, ezv.) to mean "to (do, etc.)
So, since you're not "learning in order to love your baby," just "learning to love" it, it's just te, not om te*.
I don't think I really agree with that.
You can perfectly say: ik vind het fijn om te lopen (I like to walk) het is leuk om je te zien (it's nice to see you)
and there's no real sense of purpose there and you certainly wouldn't use 'in order to' to translate it.
The word 'om' is often not really necessary but it's used very often in speech and it actually sounds a bit weird to omit it.
To me it doesn't sound wrong at all to say 'je zult leren om van je baby te houden', and I think many people will use it that way.
I'm always left baffled by how Dutch people think that their language makes the least sense whilst, according to them, German is much more logical (even though there's enough about German grammar that can't be explained any more easily).
So, I'm always wondering what exactly the Dutch think is so illogical about their language... This seems like an example where German makes more sense, though.
Still, the constant insistence that Dutch grammar is illogical whilst German isn't seems beyond ridiculous to me as long as no one ever gives an example why.