I do not have any degree. Should I consider part time study in my mid 30s?

Would'nt go all out to support a part time study.

I believe this depends heavily on your job requirements.

Personally would think a degree would not be required for hand-ons or brokerage/sales jobs (There might be a whole lot of other niche jobs). On the otherhand, certain private part time degrees MIGHT NOT get you the intended recognition despite your time/efforts/invested tuition fees/personal take aways ect ect.
I reckon it would be important to figure these main points

-What are your main strengths & weakness

-Are you proficient and confident in your current function/sector

-Could there be a chance to enrole in some of government's mid career switch program where you get some decent allowance while being retrained with other skill sets

(above usually give you high conversion rate from training to a full time job)

-research on programs that are really worth the time and money as it is recognised by the industry and/or employers

At mid 30s i believe theres a good chance to continue working for the next +/- 30 years, would be important to keep ourselves adequate for the economy but wouldnt blindly enrole myself in any part time degree programs(especially just for the sake of telling others that you have a degree), that might not really help to make one relevant in today's fast changing world.
I hope my humble opinion is of some help.

If you have the time and resources, I will suggest to go for those skillfuture courses instead.

They are all highly subsidised (90% or so) and has broad range of topics that are relevant to current demand (Data analystics, digital marketing, python)

You should go check out, there are even courses for soft skills too, like working on EQ, working in a team, communcaition skills etc

If you are planning to work for the at least the next 10-20 years or so, I think it is important to consider part time studies. Our society is developing at such a rapid rate, making the work force more competitive in the near future. Hence, keeping up to date and on par with our society's growth would be important. However, considering you have 2 kids, if part time school is a financial or time management issue, there are other alternatives. maybe you can try couses either online or with the Skills Futures Credit. Look for something that interests you while at the same time, useful!

It seems that you are making good use of skillfutute initiative. Getting a degree is certainly beneficial for you in the long term as you are still considerably young.

I would suggest you to consult your higher ups. Some value experienced more than degree. I also heard that some position needed a degree.
You need the support of both your company and your family to transit to part time study. There are more considerations now that u have a family.

Alternatively, u can opt for online learning, and online certification to upgrade yourself