as a french native speaker, here’s how I’d make the difference:

« Dans ma rue » means literally “in my street”,

this is the general (and litteral) meaning of « dans ma rue »

but when French mean “to my street”, they say « dans ma rue » too.

not necessarily, to my understanding, “to my street” is litterally translated by « vers ma rue ». But « vers ma rue » can have a few meanings like “to my street“, “around my street“, “towards my street“…

When in french we say:

• Où vas-tu ? »
• Je vais dans ma rue ! »

we really mean “I’m going in my street”, litterally and physically, even though incidentally I’m going to my street.

N.B.: I’m not sure what the difference would be between to my street and in my street for native english speaker ears.

HTH

“dans X rue” is used the same way you would use “in x street” in English when you are talking about something “in X street”.

Examples:

Il y a un chien dans ma rue. There is a dog in my street.
Il y a une voiture rouge dans cette rue. There is a red car in this street.

“dans X rue” may also be used the same way you would use “to X street” in English when you are talking about a direction, a place to go to.

Example:

Je me dirige vers cette rue. I’m heading to this street.

I think you’re tackling the problem the wrong way.

The meaning of dans depends – in English – on the verb used. If dans follows a verb that implies a movement from one place to another then in English they will use whatever verb that English verb requires, it’s usually “to” but not always.

Je vais dans ma rue. I’m going to my street.
Viens dans ma rue. Come to my street.
Nous arrivons dans ma rue. We’re getting to my street/ We’re arriving at my street. / We’re reaching my street.
Nous entrons dans ma rue. We’re getting into my street. We’re walking / driving /into my street.

If dans follows a verb that describes an action that happens within one place, or if it is just used to introduce a place, then it will be translated by “in” in English.

Maintenant nous sommes dans ma rue.
Il y a un restaurant dans ma rue.
Ça s’est passé dans ma rue.
« Où est ce restaurant dont tu m’as parlé ? » « Dans ma rue »

I think it’s a question of English and has nothing to do with French….