I Don't Know What I Don't Know

You just need a reason for the relationship to ruin the lady's happiness (as conceptualized at the time) to make a delicious romantic tragedy. Is her other suitor more wealthy? Is the blood relationship too close or touched by scandal (e.g. madness in his blood)?

If the lady's family have hopes/expectations of her marrying someone richer or of higher standing, a connection with some other less eligible suitor (whether or not he's a relative) would be extremely undesirable. Her family would likely lean on his to get him out of the way and leave the field clear for their preferred candidate.

If you want a truly forbidden relationship, Victorians liked cousin marriages, even first cousins, so that won't do. Uncle/niece marriages were known, though not well-approved. If one or the other were a bastard, people might wonder & gossip might be harsh, but there's nothing truly forbidden about it, just a little scandalous. Similarly, if one or the other brings a lot more money to the match, it would make tongues wag, but it doesn't actually break the rules, just stretch them a little.

The one truly forbidden relationship that would bar a marriage was incest between siblings. The case where siblings separated as young children came together unknowingly as adults and discovered the shocking truth too late -- too late! -- was common in folksong, a staple of popular tragedy, and it actually happened enough to be plausible & scary. Equally horrifying was the Forbidden Love between step-siblings, esp. those whose parents married later & did not raise them together.

Another common scenario: he was wastrel, or unlucky at cards, or made a series of bad investments, or etc. and blew through a big chunk of money (his own, or a prospective inheritance, or funds that the family felt obliged to pay out to keep things quiet). They send him abroad to keep him from repeating the same things that got him into trouble the first time -- break the bad habits, distance the bad companions, remove the temptation, give him a chance to set himself right in a new place.

Most of the reasons one might be sent off would likely be applicable to many historical periods. Do you want the thing that causes his exile to be specifically bad in this era? There are other options like an opium addiction, a gay relationship, a relationship with a woman of ill-repute (more than a night with a prostitute), sexually predating the servants. How bad do you want to make him?

The other question would be whether the problem that gets him sent away resurfaces later. If it's simply an inciting incident, it could be anything, but if it impacts the story downstream, you'd need to consider the options more carefully.

Fathering a child with a servant? Cheating at cards? Offering violence to his father while drunk?

benbenberi said:

Another common scenario: he was wastrel, or unlucky at cards, or made a series of bad investments, or etc. and blew through a big chunk of money (his own, or a prospective inheritance, or funds that the family felt obliged to pay out to keep things quiet). They send him abroad to keep him from repeating the same things that got him into trouble the first time -- break the bad habits, distance the bad companions, remove the temptation, give him a chance to set himself right in a new place.

Click to expand...

They also sent him abroad to get him out of the public eye, and stop him embarrassing the 'respectable' family members. A man can find bad companions, and temptations, anywhere. His absence, however, gives the family a chance to gloss over his behavior.
"Teddy's doing rather well out in America." = "At last report, he hadn't been hanged."

It could be something as "simple" as running up gambling debts in the mess hall (army officer) he never paid. Or writing bad cheques. Notions of honor for the aristocracy and upper classes were tied to not getting caught behaving badly, not to the actual behavior itself.

Think of the case of Colonel Valentine Baker: https://en.wikipedia.org/wiki/Valentine_Baker

There's a book about these men who were shipped to Canada: https://www.amazon.com/dp/1550023691/?tag=absowrit-20

Becoming the black sheep of a high class family wouldn't be extremely hard to manage. Falling in love with a lower class/foreign woman and refusing to give her up; insisting on working with your hands for a living; offending the swinish politician who can award your corrupt father a massive business contract and refusing to apologize; taking the blame for a family scandal to protect your naïve but much-loved younger brother (who drank, gambled, and accidently killed someone).... There are many possibilities.