My spouse and our two minor children have moved from Sweden and settled in Åland. I have kept my job in Sweden and work 100 percent remotely for that job even after the move. My spouse is starting a job in Åland.

What possibilities for social security benefits from Finland/Åland do we have?
You may be entitled to benefits from Kela if your income is higher than the income limit. The same applies if your spouse's income is higher than the income limit.

Your children are entitled to public healthcare based on their home municipality. If you have not registered a home municipality in Åland, you can apply for a certificate of entitlement to healthcare based on the father's (or mother's) work in Finland.

Ultimately, Kela decides whether your family is considered permanently resident in Finland. This is done in cooperation with the country you moved from. If you are considered permanently resident in Finland, you are entitled to benefits based on residency.

If you and your spouse work indefinitely in Finland, you are also entitled to other social security than that which Kela manages. For example, employment pension as well as insurance against workplace accidents and occupational diseases.

You, as a remote worker, also need to check whether your employer has applied for an A1 certificate (see above for more information about A1 certificates) as this may change the situation.

Would it make any difference if we had moved to Åland from, for example, Spain or another country within the EU/EEA instead?
No, it does not matter where you move from.