Been a 3rd XI captain and dealt directly with the 1s captain on many occasions!
Here's my 15 years of selection experience. Alot of clubs start getting polictical and make up reasons not to take player xyz, and even whole teams. Eventually you shoot yourself in the foot and piss someone off, as you can only so long go on about "key players","balance" etc. Imho the only way to select teams is on merit, as it's far easier to tell a person he isn't good enough or he's one of the best xi in your club than any other bull story.
If you have a selection committee, go to the chairman and explain what you have been told. Get the chairman/Head of Cricket/Selection to then tell the 2nd XI Captain to pull his finger out and help you. Don't go directly to his players, chances are they are good mates with the 2nd XI Captain and will just as unhelpful. The overiding principle is the 1st XI Captain has first pick of all players in the club otherwise it's not a 1st XI - don't feel afraid to tell everyone that, before and after the game.
My club has a Sat League XI, Sunday XI, Midweek XI. The best team possible is picked in the Sat League XI, the rest are given a game Sunday. If you don't make yourself available for both you (ie saturday only) you run the risk of not getting a game.If you are available both days then you always get a game, sometimes two. Everyone knows the rules and we get very few grumbles. We are thinking of getting a Sat 2nd XI for next season so things may get more tricky then.