For your first sentence, I think there is one form of the word “séparés” that you could use to capture the notion of “never [being/having been] apart” without implying (as does “séparés,” as you accurately point out) a “relationship going[/gone] bad,” and that would be its negative form “inséparables.”

As an adjective, you could say:

[On dirait que] Vous deux êtes [vraiment] [un couple] inséparables [,comme Philémon et Baucis/comme Laurel et Hardy/comme un faire-part et son enveloppe] !

(see TLFi’s entry for inséparables [as an adjective pertaining to people] below, via CNRTL):

2. En fonction d'épithète ou d'attribut, sans compl. de l'adj. [En parlant de deux ou de plusieurs pers. entre elles] Qui ne peuvent se séparer l'une de l'autre ou les unes des autres, cesser d'être ensemble, se quitter.
   Deux amis inséparables; ils sont (devenus) inséparables. Bientôt, nous deux, nous fûmes inséparables (CENDRARS, Bourlinguer,1948, p. 199).

As a noun, you could say about the same thing and even get the benefit of the “Lovebirds” meaning of “inseparables” to boot:

[On dirait que] Vous êtes deux [vrais] inséparables !

(see below, from the same TLFi entry for inséparables [as a noun pertaining to people] via CNRTL):

♦ Emploi subst. Au collège (...), dès leur huitième, il y avait eu les trois inséparables, comme on les nommait (...). (ZOLA, Œuvres,1886, p. 34).

(and finally, from still the same TLFi entry for inséparables [as a noun extended by analogy to “lovebirds”] via CNRTL, there's):

− P. anal., emploi subst. masc. ou fém. plur. Petites perruches élevées par couples.

For your second sentence, I think all the other suggestions offered so far are good, although I tend to prefer @user168676 ‘s “news of a wedding/a wedding announcement perhaps being in sight/on the horizon.”

(Although not at all intended for your serious consideration, with this preference in mind for the notion of the possibility of a forthcoming wedding announcement  , I’ve made the following feeble/totally unidiomatic attempt at a play on words for your second sentence:
"Vous n'auriez pas de faire-part [quelconque] à faire partir bientôt, par hasard?")

For your first sentence, I think there is one form of the word “séparés” that you could use to capture the notion of “never [being/having been] apart” without implying (as does “séparés,” as you accurately point out) a “relationship going[/gone] bad,” and that would be its negative form “inséparables.”

As an adjective, you could say:

[On dirait que] Vous deux êtes [vraiment] [un couple] inséparables [,comme Philémon et Baucis/comme Laurel et Hardy/comme un faire-part et son enveloppe] !

(see TLFi’s entry for inséparables [as an adjective pertaining to people] below, via CNRTL):

2. En fonction d'épithète ou d'attribut, sans compl. de l'adj. [En parlant de deux ou de plusieurs pers. entre elles] Qui ne peuvent se séparer l'une de l'autre ou les unes des autres, cesser d'être ensemble, se quitter.
   Deux amis inséparables; ils sont (devenus) inséparables. Bientôt, nous deux, nous fûmes inséparables (CENDRARS, Bourlinguer,1948, p. 199).

As a noun, you could say about the same thing and even get the benefit of the “Lovebirds” meaning of “inseparables” to boot:

[On dirait que] Vous êtes deux [vrais] inséparables !

(see below, from the same TLFi entry for inséparables [as a noun pertaining to people] via CNRTL):

Emploi subst. Au collège (...), dès leur huitième, il y avait eu les trois inséparables, comme on les nommait (...). (ZOLA, Œuvres,1886, p. 34).

(and finally, from still the same TLFi entry for inséparables [as a noun extended by analogy to “lovebirds”] via CNRTL, there's):

− P. anal., emploi subst. masc. ou fém. plur. Petites perruches élevées par couples.

For your second sentence, I think all the other suggestions offered so far are good, although I tend to prefer @user168676 ‘s “news of a wedding/a wedding announcement perhaps being in sight/on the horizon.”

With this preference in mind for the notion of the possibility of a forthcoming wedding announcement, I think you could also consider the following variation of that notion (either with or without the parenthetical "word play") to use in that second line:

Vous n'auriez pas un certain faire-part à envoyer (à faire partir) bientôt, par hasard?