Is it being unfair to argue that any future prospective NHL team in Houston would even succeed or that that region really isn't suitable for NHL hockey? The original owner of the Dallas Stars, Norm Green, made himself and still is an absolute pariah initially being coy and then relocating a beloved old Minnesota North Stars team from Minneapolis/St. Paul to Dallas in 1993 even though some sports analysts and commentators were unsure and skeptical about whether the NHL's southern expansion in early 90's would succeed in Dallas, Tampa, Nashville, and Carolina. 30+ years later, it's clear such fears were unfounded and all of those above-mentioned teams, including Florida Panthers, have appeared in multiple Stanley Cups and won one.
The Stars were and have been a huge success in Dallas but it's a big "If" to say whether Houston would eventually match it as well. The Stars owners probably like having the entire Texas market to themselves and may not be too thrilled (and likely object) to a potential expansion/relocated Houston team.
As far as any future third NFL team in Texas, that won't happen as long as Jerry Palpatine still lives and while his son, Stephen, wouldn't necessarily have his pull and influence after his death, the fact that the Cowboys are one of the NFL's top 3 most profitable, wealthiest brand names and most marketable would help the Jones' family's and their lawyers arguments and Texans' Cal McNair would certainly object to any Austin/San Antonio expansion/relocation team siphoning off large amounts of their fan bases. Austin and San Antonio are indeed big growing markets with steady influxes of out-of-state specialists, multi-national corporations, companies arriving in and bolstering their metro populations, but Texas' two biggest cities realize all too well they'd lose fans and money if either one of those cities got an NFL team.
St. Louis has had two NFL franchises relocate its city over the past 37 years and both were due to bad, naive or unworkable stadium deals (Bill Bidwill wanted his own football-only stadium, city said "No", so he decided to leave; Georgia Frontiere and Rams organization signed a bad stadium deal that in hindsight doomed the teams' future in St. Louis that would be exploited by a different owner with ulterior motives who wasnt as pro-St. Louis as she was and probably never would've moved there if he'd owned the team back in L.A. in 1994). St. Louis has had two different NFL teams and they've struck out both times in that both left after bitter, prolonged negotiations for a new stadium didnt happen and the Rams were kind of a mini-dynasty from 99-01 little less than 15 years before they moved. St. Louis might be a great NFL market, but are they a reliable one long-term past 25-30 years?