So, a paladin tank gets mana back from 3 primary sources:
1) Divine Plea
2) Blessing of Sanctuary
3) Spiritual Attunement
There are other sources such as judgment of wisdom and seal of wisdom as well. Tanking being what it is, means you probably are NOT going to be sealing wisdom. Judging wisdom is ok.
Divine Plea is by far the biggest amount of mana return for a paladin. A prot specced paladin even has a talent that refreshes Plea on melee swing. Your shields have no bearing on this.
Blessing of Sanctuary gives them mana back when they dodge, parry, block. Again, your shields have no bearing on this.
The third is Spiritual attunement which gives them mana every time they are healed. This talent does not work with absorbs. At the same time, its not where a paladin gets the majority of their mana anyway.
Now, there are two things contributing to what you are experiencing. It used to be that shields would stop warriors and druids from getting rage. This has been fixed a long time ago, but there are still hold outs that don't understand this.
The second is that a paladin doesn't get their main mana management tool, Divine Plea, until level 71. The prot Paladin's tanking tools are super mana expensive as well. Consecrate is obscene. So it can be a touch difficult for a paladin to get used to shields. Its not undoable though. I mean, I did it.
You need to make the call about how stiff backed you are going to be. Shield and weakened soul are a big part of your repertoire. You need to make the call about how much you want to deal with them being prima donnas or just bail on the group.
Edit: Just to be clear, after level 71 a paladin should stop complaining about mana. Divine plea uptime is their primary source of mana. Prior to level 71, you might want to work with them a bit, but really they should just figure out how to use their other tools such as sealing and judging wisdom.