I don't think Tom Sr has any real desire to do Royal Family activities like going to Ascot or visiting the Queen at Balmoral. He didn't even make it to England for the wedding...

Right, Markle Snr has no interest in what the royal family stands for, much less taking part in their activities. His comments and behavior are completely contradictory. I suspect that the older Markle siblings have been the bane of his existence over the years. As Markle Snr said himself in the GMB interview, his marriage with Doria broke up partly due to his workaholic nature. And that's probably why the first marriage ran into trouble too. He was obviously too young to marry and start a family with his first wife, Roslyn.
The Andrew Morton book claims (per info from Tom Jr) that the older siblings witnessed arguments between their young parents, and eventually Markle Snr left Chicago for Hollywood. Markle eventually found success as a lighting director on
General Hospital (where he met Doria), and later on
Married With Children. Morton also describes how Markle Snr volunteered many hours helping Meghan's drama department at high school put on productions. I'm sure Meghan learned a strong work ethic from both of her parents.
Meghan has shared positive experiences she's had with her Dad growing up, because she apparently prefers to accentuate the positive in a glass half-full way. But I think there's no doubt that it was Meghan's mother and her maternal grandmother who mainly gave her the solid foundation and stability to face life fearlessly and to be herself and to realize her loftiest goals. None of Meghan's goals involved marrying a prince. But serendipity happened. Anyway, it's not Harry being a prince that truly matters. It's that he's Meghan's soulmate. A lot of people do not seem to understand this, especially not the Markles.
It's hard to figure exactly what's wrong with the Markles, but there's obviously loads of dysfunction likely stemming mostly from Markle Snr not having been an attentive father. When Meghan was born that seemed to change, as Markle Snr was older and perhaps Doria was a good influence on him at the time. Doria even tried to help Markle Snr's older two children. Meghan was not born until about 3 years after the marriage. Markle and Doria married in 1979, and Meghan was born in 1981. I begin to suspect that Doria did not get much assistance from Markle Snr in helping his older two offspring, who were incorrigible teenagers at that point. Tom Jr. was reportedly more open to Doria's nurturing than Yvonne/Samantha. But ultimately, both of them were lost causes. I also wonder what Markle Snr's upbringing was like. Were there dysfunctions that existed in his childhood as well?
Again, I think Markle Snr's lack of significant nurturing of his older children rankled with them their whole lives. It must have become even worse of a bitter pill when they saw how much Markle Snr and Doria doted on Meghan. And then the older two clearly began to settle all of their rank bitterness and jealousy upon Meghan, a child who was so much younger than them. Most likely all of the Markle in-laws looked a bit askance upon Meghan in some ways. Perhaps they saw her as this interesting looking pale-skinned, nappy-haired daughter of Tom's relationship 'folly.' Yes, that's my speculation but there's evidence for this type of attitude existing among the Markles in the supercilious way many of them came crawling out of the woodwork in the lead-up to the royal wedding, referencing Meghan as if they had some kind of claim on her existence.
Maybe there was some begrudging admiration for Meghan mixed with jealousy and disapproval of her 'mixed-race' status. Here was this absolutely gorgeous child with a strong, lovely nurturing mother who loved her, and called her 'Flower.' it must have flummoxed some of the Markles as Meghan went out into the world and began to succeed. At some point, the egregious bitterness of the older siblings had to have overflowed as they put their Dad through guilt trip after guilt trip, which must have eventually begun to impact his ability to maintain a solid, loving relationship with his youngest daughter. We do know that Meghan and her Dad were not on good speaking terms before Meghan left for college, and also Markle Snr apparently did not attend Meghan's first wedding to Trevor Engelson.
It took Meghan awhile to carve out success as an actor. But when she finally hit paydirt on
Suits in Toronto, I can imagine some noses having been knocked seriously out of joint among the Markle clan.
Suits created modest but burgeoning success for Meghan. Her tenure on the show became a wonderful opportunity for her to breathe and to stretch her wings and fly amidst people who appreciated her for the marvelous person she is. For a time it was not worldwide success, but even without Harry, I believe Meghan was always destined for great things. With Harry, together they will surely make important contributions to the world in unique ways (because they both already have individually). Together, they seem to have fearless and exciting goals that are focused on giving back and on championing ambitious, caring young people.
Sadly, once Meghan met Harry, the stinky tabloid press and scurrilous media hordes descended upon the Markle swamp and began fueling their swamp creature brouhaha. By providence, Markle Snr had remained incognito in Mexico for most of M&H's courtship, and perhaps Meghan being in contact with her Dad fairly regularly served as appeasement for his huge ego, pride and vanity. And perhaps at that point Markle Snr was still not on good speaking terms with the older siblings. Unfortunately, after the M&H engagement announcement the paps ended up locating Markle Snr, and his sanity eventually spiraled out of control. Once Samantha got her hooks back into Snr, it was endgame for Meghan being able to hold onto a connection with her Dad. It boils down to bitterness, anger and jealousy on the part of the older two Markles. And I think guilt, pride, vanity, stupidity and a bit of mental & emotional instability on Markle Snr's part.