Disclaimer : ok even more than my other ideas this one would require serious coding, and may be more a sugg for a DLC or RGT2 (created a separate thread as it's a complete new system, not some little tweak/improvement).

If you read the biographies of most bands, especially those failing to stay united and reach their potential as professionnal rockers, the private lives of the musicians making some renounce their carreers for their family life once they have childs, or creating tensions between members due to love affairs is often a big factor, and IMO keeping the band united despite the musicians lives evolving should be one of the main late game challenges.
Here my ideas how it can be integrated.

a) beginning of the game
To avoid adding more complexity to early game, all (or at least most) musicians would start single, so no big change.

b) meeting partners
Usually love affairs would be between musicians and their fans, so activities making the band gain fans (busking, gigs) would come with a chance based on the number of fans gained, that a band member encounter a potential love interest (if this band member is the main character he would have the choice not to start the relation ; other band members would have chances to start one based on their traits, with event text describing the outcome "A lovely woman spent her time trying to grab your bassist attention but being such a perfectionnist he stayed focused on his music and failed to notice her".).
Out of that more special and usually disastrous love affairs (ie between a musician and someone not interested in music who will spend her time trying to convince him to abandon the band, between two of your musicians -directly giving inspiration bonus everywhere but disastrous if the relation end or reach the childs stage-, between a musician and another's girlfriend travelling with the band - see later) may eventually be started by rare events (won't detail these special cases too much as it's going to be a big wall of text already).

c) stages of relation

Relations would progress (and sometimes regress) through several stages (here I have the idea of 5, there may be more or less).

1- In the first stage of a relation ("love interest") the musician partner would continue to live her/his own life in the town where the encounter happened.
The boyfriend/girlfriend would so appear on the map (an icon near the city with mouseover "Here live Jill love interest of Joe Shmuck your drummer", and relation will only progress if the band spend time in that town.
The musician would naturally be happier to spend time there and gain a stress reduction bonus for every free hour he has in this town, he will also be inspired and gain a bonus to his performance when he plays or write songs there.
On the other hand affairs may end fast in this early stage, so the love interest would have chances to disappear every week the musician spend away from town, and he may also encounter someone else on the road, with normal chances to start a relation (let's say a musician may have up to 3 or 4 at a time at this stage - ideally with personnality traits influing that, some musicians may be don-juans having lots of affairs some more the beta type focusing on one).

2- That would change once a relation reach the second stage (relations would have a small chance to progress every day the musician spend in a love interest town), with a love interest becoming "boyfriend/girlfriend", and all other relations ending.
The boyfriend/girlfriend would still be localised but travel a little more to meet his/her lover and so the relation bonus and potential relation progression would be extended to all cities in a range (say a range coving 5-6 cities in average).
But being more attached the musician would also start to have maluses, with increased stress and lowered performances the more time he spend out of this range, and while the relation may regress to simple "love affair" if he spend a long time away the musician would consider band leader responsible for the schedule having damaged his relation, raising tensions in the group.

3- The next relation level, say "couple", would open a new option to the player, have the boyfriend/girlfriend travel with the band (ideally make the character appear on main screen).
While it would give performance and stress reduction bonus to the musician everywhere it would come with serious downsides : the band would have to give some support job to the partner, paid half the musician salary, and also girlfriends/boyfriends travelling with the group would have chances to trigger several bad events generating important tension (jealousy if one musician is allowed to have his partner with the band but not another, love affair between a single musician and the girlfriend of another -happened to the best on the road, see rolling stones biographies-, the partners of 2 musicians not standing each other and creating tensions between them, etc...)
The player may also chose to refuse, in which case the boyfriend/girlfriend would stay localised on the map, with same range as in stage 2 but increased maluses if the musician is outside.
Finally not all couples are made to spend their lives together, so even if the musician spend time with his girlfriend/boyfriend the relation would have a chance to end instead of progressing more at this stage, an event that would seriously depress the musician for some weeks (I'd say about half relations shouldn't go past this stage).

4- If the relation still progress, the couple would consider wedding.
Wedding would come with some serious initial cost, as the musician ask for advances to buy a house and settle with his husband/wife and spend a week in honeymoon, but then give the relation bonuses to the musician everywhere without the downsides of "girlfriend travelling with the band".

5- The main downside of wedding would come with those unfortunate consequences called childs (an event having a chance to happen every month if it hasn't happened in the last 9), changing the married musician into married with child(s) .
While making the musician ultra happy/inspired when he can have a day off with them, childs (the more you have) would also be a large source of bad events including occasionnal huge stress rises (just before their birth, when they look unhappy, etc), surprise needs of days off / missing of dates due to a child being ill / having to babysit him, and finally make the musician reconsider his life style triggering increased costs if the player wants to keep that band member.
Depending on his traits, his pay, his number of childs (would only start to become a serious risk once he has 2 or more, so really late game), the success/activity of the band (of course would be less likely to leave in the middle of historic gigs in New York) and his traits , a musician would have a chance to consider retiring to take a more normal job allowing him to see his family more every month, in which case the player would have no other option than to offer him a large pay rise to convince him to stay longer, or search someone else more ready for the adventurous life of a rock band (finally making recruitment interface useful past the beginning of the game :).

TL:DR - happy love life give inspiration bonuses to musicians but the more they progress the more they may generate big problems for a band, from depressions when they end to clashes due to jealousy, and even members considering retirement once they have childs.