I'm presented with a problem I'm quickly realizing that I may have inadvertently created:

I have a group of PCs who are all working together to take down a Thieves Guild who have all impacted their lives in one way or another, (Stolen family relic with immense power needs to be obtained and brought back home, bandit captain killed their family (classic revenge story), need to retrieve relic for a rich noble for big reward) But one of my players (a ranger who may or may not be planning to multiclass into druid) is on a mission to return some Owlbear Cubs back to the mother Owlbear after being stolen by the thieves for power and monetary gain (sell them to the highest bidder for profit). While it sounded good on paper, I'm realizing that time is going to be a factor to get them back to the mother and have it still make sense. If I drag out the story too long the "cubs" will be adult Owlbears by the time they reach them and either have killed off their captures on their own, been killed by the captures when they realized they couldn't control them anymore, been sold by the thieves' guild, or the mother will be dead by the time the "cubs" return home. 

So my question is two-fold, if I create the redemption of them getting the cubs back early and my ranger fulfills her quest, then what do I do to keep her on the adventure if she wants to keep playing OR, if I delay the safety of the Owlbears until a later time, how do I deal with the time frame it took to get the "cubs" back to the mother without making it seem like haven't months or even years gone by and these "cubs" are still cubs?

Have the party get word the cubs are being transferred (or have been transferred) to the party that has paid the thief guild to abduct them. Upon successfully saving the cubs, the Ranger discovers other animals that have been abducted.  Further interrogation of guild member reveals a lucrative business of the guild in abducting animals, and they currently have multiple contracts with various parties all over the continent. They could have ships at the docks that illegal transport creatures; they sell illegal products made from fats, fur, hides of these animals, etc. 

So the Ranger (and possibly a Druid) can now have a cause to take down this criminal enterprise to prevent the illegal trafficking of animals. 

Thats a great idea, it fuels into her love for animals and her desire to protect the forest from all threats and gives her a reason to stay and continue with the mission and bring her new friends along to help her. 

Petepan has a good idea for tying it all together in general. For this specific instance, I’d say don’t change anything about the owlbears. The character, and party, will need to make a choice, and there will be consequences. Personally, I enjoy giving a party options where they can’t possibly do both things they want to do. It makes the choices generally more impactful. They should know the guy isn’t going to stand there with an exclamation mark over his head until they decide to interact with him; the world will move on.
And, it lets you fudge things a bit if you need to. You do it this time, and they can only do one mission. Then if the situation comes up again, you might decide they can do both, but let them think they’ll only be able to do one. Keep them guessing. 

there's nothing in the basic rules that says a creature dies or even ages while petrified. maybe the animals are being turned to stone for transport and auctioned as art to fool anti-poaching authorities.

that feeds into the later obligatory gladiatorial arena where the ranger and friends are pitted against the same sorts of animals they'd prefer to set free (inevitable, right?). include some chaotic loon villain safe above using a miniature catapult to fire off potions of restoration (among other things like glue and bbq sauce) to set free randomish statues amongst a veritable forest of potential monstrosities. definitely describe a few that are recognizably way too powerful to fight (and then mercifully leave them off your actual encounter list). roll some dice! it'll be great!