1- Dwarves are the masters of the deal... when they set their sights on something that can be bartered they are as studious as they are hardworking. Lets use the half orc female... Lets say she was the product of the Orc chieftain... Lets then extrapolate that the mother was a clan friend. They would feel compelled to aid their friend the human mother might have died in child birth leaving the half orc to be raised by the dwarves. Being the product of the chieftain she holds two values for the dwarves... child of a friend and a heir to that orc tribe.
2- Female Orcs even half orc females have one aspect only they can do for a tribe .... Have children... If the half orc child was raised and then mated with a Orc or a human and produced a child that male child could challenge for leadership. Making the female half orc an investment for the future one a dwarven clan "could" be willing to invest in. When I say the female half orc could challenge for leader ship this was what I meant. Dwarves will long outlive orcs and half orcs... the investment of keeping one for the chance to produce a heir to an Orc tribe in the future could be something appealing to a dwarf tribe especially if they are out numbered or hard pressed to fight off the orc tribe.
There are many different ideas that can be explored.
I do agree just finding a half orc female somewhere and a dwarf male just happens to fall for her is far fetched.... But there are ways and viable reasons a half orc female and a dwarf male could be in proximity to build a relationship. The biggest hurdle would be the alignment of the dwarf... because going against Clan taboo would be a huge huge hurdle for the dwarf. The alignment of the dwarf as well as ... how he really valued dwarven ways would be called into question. I still think there are ways and reasons it could happen.
The one thing that doesn't need much explaining in my opinion is the Half Orc falling for a dwarf... Half orcs by nature are constantly trying to find a way to fit in somewhere. I think half orcs are vulnerable to a great many things because of their nature to try to fit in. Again the dwarf would be the one making a huge leap away from Clan values not to mention dishonoring his family... It would bring a great shame to his own Clan honor. If he choose to do this I wonder would he be sneaky in that ... he choose to leave the Clan to choose his forbidden love? This is the part of that forbidden love that intrigues me and catches my attention. The Dwarf... and how if would shape him. Would he choose to be honest thinking it would keep his honor in tact? Would he choose to sneak away? If he snuck away would this bring hurt to the half orc girl? She wasn't worth claiming to his clan? If he is honest would the half orc girl feel guilt and shame for the pain the clan inflicted on the dwarf? I don't see anyway the Clan would be ok with the dwarf... There are a lot of ways that this could really flesh out the inner workings of a dwarven character ... The half orc female getting fleshed out would require figuring out all the dwarf stuff.