You can join as many credit union as you like. Be aware most credit union "hard" pull your credit report even if you don't app for a credit card or a loan.
What are you worried about in joining a second credit union? Spreading your balances too thin? Another hard inquiry? You're probably fine, but you've got some work to do before you get a good card / auto loan rate / etc.
What would you recommend?
Depends on your goals. If your goal is to get a CC, then some CUs offer CCs that are easy to get with a lower score. Some CUs offer higher limit CCs. Some CCs are hard to get by some CUs. YMMV. And some join for the benefits offered by that CU, like getting your EX FICO from PSECU. And ditto, you can join as many as you want. I belong to NFCU, Penfed, NASA, and a local one here, though I only have one CC from a CU and that's NFCU.
Member of 3 CUs. 2 CCs from the 3...one is by far my highest limit, the other is by far my lowest.
I am probably pitching in too late, but I still want to add my quarter cent
The only thing not so great about CUs is that they almost never have good rewards programs on their cards (excluding like 2-3 or 5 CUs) so though many of them may be great for mortgages/auto loans, you always need to be careful about how many CU cards you end up having.
I would suggest a local CU and one of the folowing-NFCU,NASA, Addison Avenue,Alliant or PENFED-I'm a member of NFCU,Addison, Alliant, and NASA-have credit products w/NFCU and Addison-I've also heard that CU's are great for a Mortgage/Auto Loan(as the OP stated earlier)-as far as rewards,my Flagship Visa is pretty good