Give it 2 full working days, if not approved by then, I'd go. You can be up to 7 days late if you do it in person. My last online took 2 working days ,did it last month.
. Always pays to go at least a few days early for extensions, this is a classic example why. Forgotten or incorrect paperwork can cause same issue, yet alone funds.
My situation was a little different . I was due to return to Australia same time my yearly extension was expiring. Was going to get a new visa in Aust and return on that because of funds, (much lower financial requirement ). 4 days before I was due to fly out my wife was rushed to hospital. I wanted to stay here for her but didn't have the 400k in 2 months. Went to immigration and explained situation. They bent over backwards to help me and said that I can have a 60 day extension. I organized the 400k immediately and when the 60 day ext was due to expire they gave me another yearly spouse extension with no issue. It's all about being prepared for the unexpected. Going early buys you time.
. I have personally done this for same reason.. Yearly spouse extension -> 60 day visit family extension -> yearly spouse extension. As said above you can only use it once per visa/extension combo.
If you've left it to the last minute and the 60 days isn't enough to fill the funds gap then you're out of options other than getting a fresh visa from outside Thailand and re entering to buy the extra time. This was all explained to me thoroughly by a senior imm officer at Changwattana face to face.
. Give your son and his friend your home adress before they arrive, on the very remote chance they are asked at passport control. On my first ever visit to Thailand on visa exempt I was asked for it because I didn't have hotel details and was staying with a relative working here. This was a long time ago and once I provided the adress it was fine.
. Might pay to do some background research on your sponsor first. I've heard many stories of the "guaranteed work placement" not coming to fruition once study is finished. It's been used as a marketing tool for "schools" here to get quotas. Ask for proof and or examples. If they hedge, I would be wary. Same scheme has been used here for internships, which is unpaid work in the future.