Bonjour,
I think first part concern an common object (or concept) : “avec une femme”.
Second part is more “human” and concern a specific person.

Illustration :
“Elisabeth à qui j’ai donné mon coeur, est une femme à laquelle je ne peux échapper !”

But sometime you can also make an objet more like a person : “Cette femme à qui j’ai confié mon enfant …”

In your context, you could use both, as pointed by Laure in comments.

However, I think this is simply a basic rule of writing here, not to write two same formulations in the same sentence.

So

Grâce a toi, je suis avec une femme à laquelle je me dévoue entièrement, à qui j’ai donné mon cœur.

Grâce a toi, je suis avec une femme à qui je me dévoue entièrement, à laquelle j’ai donné mon cœur.

are absolutely correct. However, the formulation "à qui" only refers to a person; this is like saying to whom in English. Which means

la fleur à qui je pensais

is incorrect. You have to say

la fleur à laquelle je pensais

Technically, laquelle and qui might be used in either or both case in your sentence.

Grâce à toi, je suis avec une femme à qui je me dévoue entièrement, à laquelle j’ai donné mon cœur.

However, one slight difference is laquelle usually means “one from a known set” while qui has not this restriction and is then open.

See the difference between:

– À qui vas-tu offrir ces fleurs ? → The question is open, anyone might receive them, including more than one person or just nobody.

– À laquelle vas-tu offrir ces fleurs ? → It is assumed by both parties that a list of potential receivers is known and one and only one of them will get the flowers.

This explains why the first sentence is the one that would probably be the most natural. Moreover, French tend to avoid repetition so your second suggestion would be also less likely to be used.

When following a preposition like à, pour, vers, de, avec, sans, etc., the pronoun qui is restricted to living beings, whatever their gender or number.

On the other hand, laquelle refer to singular and feminine word which can be a living being (qui), a thing (quoi) or a location (où).

‑ À qui est cette voiture ? (Whose car is this ?)

‑ À laquelle (d’entre vous) est cette voiture ? (if said in front of a group composed of men and women, the question is not directed to the men)

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‑ À quoi j’ai droit ? (What am I entitled to ?)

‑ À laquelle/Auquel ai-je droit ? (Which one of these am I entitled to ?)

‑ Où tu descends ? ( Where will you get off ?)

‑ À laquelle tu descends ? (At which one (of the stops/stations) will you get off ?)