In fact, Spädbarnet vill gå till sin mamma would not be correct, since the baby cannot walk, and vill gå presupposes walking on foot (not necessarily walking all the way, but some walking must be involved – Jag vill gå hem means I want to go home, but you can't say that unless you intend to walk some of the way. Let's say you're in New Zealand and want to go home to Sweden: walking will not be a significant part of your returning home, therefore you can't say Jag vill gå hem in that case, you'd have to say Jag vill åka hem – however if you're at a friend's house and you want to go home, you can say jag vill gå hem even if you're going to drive or take the bus, as long as you're focusing on the leaving part, where you'll actually be walking out the door).
We very often say vill + direction or goal, to indicate that we want to get somewhere without specifying how we'll get there.
We do use gå a lot, more often than the constructions without a verb. It's a question about focus. Like, Det är dags att gå till skolan 'It's time to go to school.' Focus on getting up and leaving. – If you want to go somewhere abroad, you'd most likely say Jag vill åka till …, 'I want to go to' …, but you can also say Jag vill till … if you focus more on the goal.
Maybe you have less restrictions on go in Dutch in cases like this, at least English has. As far as I can tell, vill till sin mamma is pretty much the only option for an infant in Swedish, since åka doesn't really cut it either… Well ok, there's one more, komma could work too. Han vill komma till sin mamma, ’he wants to come to his mom’.
Because "wants to his mom" is not grammatically correct in english. If you say to in this context you need some form of verb. The baby want to BE WITH his mom, the baby want to GO TO his mom, the baby wants to BATTLE his mom... etc. If you mean "wants his mom" I think it wouldn't be accepted because that is not what the Swedish is saying. As mentioned above it may be focusing on leaving where he is to go to his mother instead of wanting her in general.