Hey Yuri, welcome back to eve - and congrats on the little one 
It sounds like our corp, UMAH, are would be a good fit for you.
We are a null corp based out in Syndicate, a mixture of indy, pve and pvp players spread across EU/US/Aus time zones. We are a fairly small corp in a phase of expansion, but are well established in our space and playing a very active role in our alliance. It sounds like you’re looking to get into PvP while maintaining a steady income - fortunatly there are plenty of income streams to get stuck into in our space. PvE wise we have access to level 4 missions, burner missions and plenty of space for combat anomalies + exploration in our region and the surrounding area. We also have a pretty great industry infrastructure set up across our space, a large BPO library, offer plenty of moon mining (including several R64 moons), a corp buyback programme, and most importantly an active and engaged membership who are here to help 
We have a small base in WH space, if you want to dabble in that, too.
PvP-wise we have lots of opportunities, roams, gate camps and drop etc., including CTA’s which we encourage all our members to join in with. There are lots of experianced pilots to help out learning the ropes PvP-wise, and pilots with connections to other alliances who actively get us involved in larger pvp roams etc. from time to time.
In terms of our membership, we are mainly adults – many with families – and we’re not interested in drama; with that in mind our only real rules are:
i) no smack talk, racism, toxic behaviour etc. - we are all here to chill out and have fun flying pretend spaceships, at the end of the day
ii) real life comes first, always. That is the principle at the core of our corp - it sounds like that is somthing you are on board with.
If you decided you did want to join, our alliance has a programme for ordering construction of ships, modules, ammo etc. within our region. We also offer a JF service to highsec, if you need help transporting stuff in/out of our region.
If you like the sound of what you hear, then the best way to reach out is to join our public channel - UMAH_Pub. If not, I hope you find what you’re looking for!
o7