@Ozeire I would just like to re-enforce what others have said here. This is a change for a new beginning for you as a family so you need to be very careful about how you do it. First thing, before anything else is to pay down all your debts - totalling 20k. You should try and get a haircut on those numbers, so negotiate hard with them. Tell them you are thinking of moving back to Australia and would like to clear your financial situation before you go, and ask them if you are to arrange a single settlement now what would the figure be. Innocently ask if the debt is secured on anything? Its likely its unsecured debt so they may be willing to negotiate on it. Personally, I would be aiming for at least a 10% haircut, especially on the credit cards.
At that point, look to put at least 15k away into an account you have to make a very conscious effort to access, ideally send a letter in writing to move the funds to your current account. This needs to be the emergency fund and needs to be treated for real emergencies as discussed above. Ideally two signatures needed to transfer the money across to avoid temptation.
This leaves you with 10k roughly. I am not going to say not have a holiday and not visit your family in Australia. I am going to say the opposite and go do these things, just be careful with the timing. Also consider the type of family holiday you want to have with a 2 year old and a baby. The baby is easy to travel with - the 2 year old much more difficult. Also think of when/where you want to go, the heat of the summer months and the massive premium cost of peak season between June and August (inclusive). I would suggest mid-late September or early October as it can still be quite pleasant for children and there are good deals to be had. The trip to Oz I will leave with you
But do see if there are any airlines which offer very cheap fairs to 2 year olds and be careful of the childs birthday on the return date !
I would not say to blow the 10k on this though, and try target at least 4k or so left over that will be used solely for annual expenditure such as health insurance, car tax, insurance, car service etc. The trick is then to pay 350 a month into a regular savers account, so next year you have another 4k to pay the annual expenditure and keep the cycle going. This assumes 4k is your budget for annuals.
Irrespective of the inheritance, a critical step though is to do a proper household budget for the family, taking into account all monthly, annual and ad-hoc expenditure. As a family you need to understand where your money is coming from and going to. There is lots of talk above about saving and later dipping into it, starting PRSA's etc. You need to have a proper financial plan to show yourselves what your options are, how much you expect to have left each month (and the regular savers for annuals is a monthly expense) and you can then decide what to do with it - whether it be save it or put it into a PRSA.
I think you seriously need to consider what your childcare arrangements are and what will work best. There is a chance that a one income family may actually work better for you in the short term - no idea in the long run as it depends on the careers you both work in. Keep in mind the transfer of tax credits, the home carers tax credit etc. You need to do the maths to see how it works. Having two in childcare at the same time is expensive, and also need to understand if one is sick etc who is taking the hit to mind them. Its not easy and it really cannot be left on one persons shoulders to take the full childcare burden when they are sick.
The final point I would make is your spouse has 100k life assurance cover. You have two children under the age of 3 who are likely to be dependents for the next 20 years. That works out at around 5k a year. Is this really sufficient cover ??
Pensions are also a concern, but probably harder to fix in the short term. You are not unique in this regard.