I had a lot of the same issues, being a single father with a demanding job for many years.
Work Out A Sustainable Cadence
Weekly may not be possible in the end. Figure out how frequently you can realistically attend, and ideally how to make that a regular schedule not random (because it's harder for people to accommodate random). Ways to up this:
You need to have a discussion with your wife and say you need regular time for a hobby. Negotiate what this could look like. Maybe you need to swap off "off periods" so you both can have a hobby, or pay for a babysitter and so it's also Mom's afternoon off, money allowing. When I was single dad of a very young child in a new city with no social support I could swing paying for a Sunday afternoon of babysitting every other week, so my cadence I could play was every other week.
It's hazy what is preventing you specifically from attending - what does "wife is unsupportive" mean specifically to the situation? You need to break it down to the tangible issues. Is it that she wants to leave during that time and you're on child care duty? Or she "just wants you at home" for ineffable SO reasons? Then see if attending remotely is an option. My group had a member move away but he calls in via Google Hangout for a game every other week. Maybe your group isn't up for this, but that part comes next. You have to first clearly understand what your blockers are, and figure out what options you have. If it's "your wife expects you to participate in randomly planned events," then you can negotiate timing of those events or figure out if weeknights are better than weekends for you for gaming or whatever...
Come up with options of what you can do.
Find Out If Your Group Can Accommodate, Or Find One That Can, Or Found One That Can
Now that you know what you might be able to do, talk to your group and see if they are cool with that. If you can't attend weekly but can do biweekly, maybe they'd be open to alternating weekly campaigns (my gaming group does this for that reason, not everyone can do every week but some can, so we run 2 campaigns and some opt in for one, some for the other, and some for both as their lives allow).
See if attending remote is an option, and so on.
If there's not really a way to work it out with the current group and campaign, see if maybe there could be another campaign with some of your current group, or maybe even a totally new group. I know my gaming group has a lot of "spinoff" groups - this guy runs a game for a bunch of other people Friday night, these two are in a game with someone else - it doesn't have to be "These six people in this one campaign".
In fact, if you can't commit to a cadence, maybe more one-shot or pick-up gaming is what you are going to have to do.
Obviously all this is dependent on the other thing you need to break down and figure out, which is what you want. Where's your joy coming from? Gaming in general? This group in particular? D&D? Campaign play vs. one-shot play? Rank your desires. If there was a totally different group willing to meet whenever is good for you, is that your next-most-optimal scenario? Again, clarity is your friend here. Once you have that, then the group (existing and others) can also decide what they can do, and you fit your needs and their needs together.
Stay Plugged In Even If You Can't Attend
The answer may end up being "I want this group and I can't work out attending too much more and so this is my life now." But there's things you can do to participate somewhat even if you're not present.
First, if anyone's willing to write up session summaries, you can follow along that way. My group is in the habit of doing pretty long session writeups and we publish them on my blog, some are even like 12-page pdf types. This is fun and one of the corollaries is you can read them a bit as if you were there. This obviously requires someone to be willing to do this (though you can do it when you attend).
Second, even if they're not up for you attending remotely, maybe you could still listen in remotely. Via recording or even just via "hey put someone's cell phone on speaker and set it in the middle of the table and I'll listen on airpods as I do my honey-do list." A live podcast of your own game! I haven't done this for gaming but do it for work meetings all the time. "Here, watch on your own time."
If they are running your PC as a NPC while you're gone, you could ask them to text you from time to time with critical decisions or looking for pull quotes. Or just tell the DM ahead of time things you'd like him to say or do, so you can keep some things going in your absence.
Anyway, best of luck, you will probably have to give something to get something as part of these negotiations and tradeoffs, but if you can be crystal clear about what the hurdles are and what things you can/are willing to do, usually finding a solution isn't that hard.