Hi and welcome!
Taking that as the 72K displayed on the share your salary topic, that’s about on par with what my understanding is of what a civil engineer working on roads or hydraulics (no idea about structure) starting their career, or a 30 something geologist would earn in Wallis. There is a good margin for progress and it certainly makes things difficult for you with a family of 3, but I would not consider this a poor salary as a matter of framing my situation, even though the path forward probably involves increasing your income.
My bet is a lot of master’s degrees lead to that kind of salaries at least for the first few years of their career (which, at 30, is probably kind of at the margin of where you still are). I wouldn’t focus on my degree of education when considering my financial prospects in Switzerland. There again, it’s mainly a matter of framing but framing helps muster energy or nourrish despair so it’s an important part of the journey.
As an alternative to changing field, you may also consider working for the public sector (if you aren’t already). They can’t compete for the highest paying jobs (a business owner or someone with big responsibilities will make multiple in the private sector of what they could make working public) but usually offer better paygrades for people in what may be your range of qualifications.
That’s not bad at all at 30 with a single income 3 people family, congrats!
What is the Genossenschaftskapital in?
I’d start by trying to build trust and confidence, being on the same page is important. In your situation, and in order to get your wife on board more easily, the baskets approach may make sense.
I’d start by sitting together with your wife establishing what your expectations are, as a family:
for the present: are you happy with your lifestyle? What amount of spending would you like to be able to afford? Are there specific purchases/expenses you are targetting (you have mentioned buying a house)?
for the future:
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what kind of lifestyle do you want to be able to support in retirement? Does your wife think and plan that you are going to receive the max AHV pension in retirement (spoiler alert, chances are you won’t if you keep on your present track).
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what kind of life do you want to offer your children? Does it involve availability and spending time with them? Will it require funding certain activities? Also, what role models do you want to be?
This is important to set expectations: your wife may be thinking you can afford comfort that you realistically can’t and won’t be able to working your current job and putting extra savings in a bank account. It’s also important to know and agree on what your minimal safety level should be, and to make sure that that level, at least, is guaranteed.
Regarding that point, I’d start by looking at my insurance coverage situation before getting to investments. This would help both of you feel safe, protect your family against hardship and build confidence in your ability to invest and not need those funds for the coming years.
Step 1 would be looking at your pillar 2 statement and figure out how much:
- You would get in case of disability.
- Your wife would get in case of untimely death from your part.
- Your children would get in case of your disability.
- Your children would get in case of your death.
Also check if that coverage is linked to the amount of the savings part of the policy or if it is a fixed amount based only on your salary.
Step 2 would be checking your situation with AHV-IV to know how much you would receive in case of death or disability, also in retirement. You can ask for a statement (there’s a limit to how often you can do that but I’d definitely do it when first starting to assess my financial situation): Statement of the individual account | Leaflets & forms | Information Center OASI/DI
Don’t forget to ask one for your wife too: raising kids gives right to AHV bonuses that you don’t want to miss on: https://www.ahv-iv.ch/p/2.03.e
Step 3 would be to assess if your current coverage in case of death or disability is sufficient. If it isn’t, then the answer is a term life insurance policy, covering risk only.
Step 4 would involve a nice relaxing weekend spent together in a resort (or whatever place where you can do activities you enjoy and that take you away from your everyday life) in order to cement that you enjoy spending time together in an unstressful life. That should help illustrate the time-value of money and emphasize that living a stressful life is not worth the cost. Financial independance is worth it because it makes moments like this possible more broadly, it is a stress-be-gone spray. That’s important for your wife to realize.
Step 5 is when you start pondering about investments. I’d make it simple, on the basis of your Pillar 1 and 2 statements, assess if you can afford the lifestyle you want to based on your current life (chances are your retirement prospects are worse than she is imagining, which would warrant taking steps toward earning more, saving and investing). Have her read (and read yourself if you haven’t already) a few texts:
Bill Bernstein’s If you can (written for americans but easy to translate into the swiss system)
JD Roth’s How to be happy and the relationship between time, money and happiness
Big ERN’s Things that keep us motivated
Mr. Money Mustache’s Zero to Hero
Let us know if you require literature in a specific language, the FIRE movement is international, chances are useful texts exist.
Step 6 is to start talking about investments. What level of comfort would she feel confident with? What asset classes are ok? Does she trust you with an active management of your assets? Would she trust you with executing a passive management of your assets? Do you need to use a third party in order for both of you to feel confident about it? Maybe it would make her feel better if she was the one to execute a passive management of your assets, would you be ok with that?
Step 7 is to write an IPS that you both agree with: Investment policy statement - Bogleheads
Step 8 is both of you researching investment vehicles that fit your IPS (or just you if she expresses an unequivocal will that you are the one tasked with it). In your situation, I’d not brush away the here-dreaded insurance investing products: while they are riddled with fees and offer lackluster returns, they do offer guarantees and management by a third party which may make your wife more confident about your future.
Step 9 is to create the accounts (I’d do it together to have her involved in the process and build her trust and confidence) and execute on the IPS.
Step 10 is to hold regular meetings (annual would be my chosen frequency) to keep both of you appraised on what’s going on and cement both of you being onboard with the plan.
Also, never ever be afraid to come back and ask about a particular investment before putting money into it. There are a lot of scams out there, we stand stronger together. 
Edit:
Reacting on that very important remark from @TeaCup, one question I would also ask myself, to which the answer may vary depending on your personality, your wife’s personality and your relationship is whether you, your wife or a third party should handle your investments. We tend to think that being a man involves taking these kinds of responsibilities on our shoulders but it isn’t necessarily true. Being an adequate man involves the wisdom to look at things how they are and to take the required steps to make them go in the right direction. This may involve you taking the lead, there are some couples for whom it wouldn’t.