Thank you very much for your response and review of my predicament!
I was sending the payments to hashflare.io and read that their 3rd party BTC processor had a 120 minute window which I definitely did not meet and was not necessarily my fault.......but what happens now?  Sounds like with hope, they'll accept the delays and provide a refund or process the 2 payments into a larger one?  Or I made a donation which is rather more than I can afford at this point.
I do have a written request submitted via their ticket process for a review of what happened but wasn't sure how the technicalities mattered.  So thank you for the clarification!

Bitcoin Client Software and Version Number: ?
Operating System: osx
System Hardware Specs: standard
Description of Problem: sent 2 confirmed transactions to same wallet address; no delivered status
Any Related Addresses: 38ZV5Zkhg2omSCJtvgTWjDncTmL1C9E6ao both sent here
Any Related Transaction IDs: ae0274bc973ef4498ba771b9799390d33e69ce285f9ae7e06fa6a972e205c2af && cd564a2b3f9db5deb0f01424c3ff0b5b8f176b47651ae571b0ffd93f1db9cca5
Screenshot of the problem:don't have
Log Files from the Bitcoin Client: don't have

ok, noob here...and i'm nervous about what i've done.  
I've initiated a cloud mining contract and attempted to send BTC to the address 38ZV5Zkhg2omSCJtvgTWjDncTmL1C9E6ao.
I believe I've submitted the specified amount in BTC plus mining fees.
I watched the confirmations in the blockchain explorer and it appeared to have been accepted; however the output states 'unspent' which I relate to as undelivered.  Is this the case?
After reading about other horror stories about other transactions not getting confirmed(and other ways to accelerate confirmation which I felt didn't apply to this case), I made another attempt(I know, stupid me) to send another payment as I felt that I didn't include enough miner fees in the first and that the 2nd payment would get processed(with a padded fee) and replace the first...well..........I sent the 2nd payment from my hardware wallet and the first from an exchange account so I know I goofed that all up from a double payment perspective.
Anyhow, I'm not worried about the double payment(because I'd request to apply the 2nd payment to supplement the 1st) as much as both are now 'confirmed'(I think) but not paid/sent?
In case the recipient cannot or is not going to accept the payment, is there a way to retrieve the 2 payments?
Or is it simply a waiting game as they're processing of payments is in intergalactic delays and will eventually get into their wallet?
If the recipient will eventually receive the payment, I'm completely fine with that and will continue to stand by...but if those payments will never get delivered to anyone, then I'd like to recover them and try again...or not try again lol.

Of course, the cloud mining account I opened shows that the account is still pending funding.  Not sure if I missed any window for funds to be xfered into the wallet address they provided as the first 6 confirmations on the first payment took over 6 hrs.

What is the procedure in this scenario??... to either stand by or accept loss of funds or other means to recover?

Thank you in advance for any input as I have googled, searched, etc for this scenario but have been unable to find an experience which is close as all I've seen were results for 'unconfirmed' transactions.