Clearly there has been a major issue in the past, otherwise, you wouldn't have two people against you, and your wife's reaction this time around wouldn't be so severe.
You have to be in the house when your wife is working as there needs to be someone there with the kids when they are asleep. So clearly an alternative such as gym or another activity away from the house is out of the question. It seems reasonable to me that gaming might be something you could do when she is not there and the kids are asleep. Although from your history, I'd say being seen on the PC when the Mrs is in the house will be a red rag to a bull. It would not go down well, I suspect. If you're on it when she gets back from work, she could very well kick off too. Also, you couldn't allow it to affect your work or mood, say, by staying up late on it and not getting enough sleep.
I have a few questions, obviously you don't need to answer to me, but maybe worth considering in your own mind.
- Is there an underlying cost issue here as well? A worthwhile gaming PC will easily be the best part of a grand these days, if not more with all the peripherals/screen etc. This is a big family expenditure to benefit just one person.
- Why is your mum getting involved in this? The marriage is between you and your wife. Although, on the other hand, you could have an ally in her. Maybe you could work the angle with your mother first, she might come around and convince your wife to give it a go.
- How old are you, if you don't mind me asking? When I got to around 30 my interest in games dropped off significantly and it seems to have been a common theme with some members here. I can barely manage more than an hour these days and almost never complete a game. The shine has definitely worn off the hobby. I am trying to force myself to complete just the story part of GTAV. I don't really know why I'm forcing myself, I just feel it's a game I should complete.
- Do you demonstrate other addictive behaviours like excessive phone use? Could this be worrying your partner and mother?
For what it's worth, I upgraded last year, full overhaul. By far the most enjoyable part of the experience was researching the parts, looking at benchmarks and adding to/emptying my basket several times and waiting in anticipation for the parts. When I built it and fired it up for the first time I installed a few games, went "oooohhh, woooowwwww, so pretty and smooth" for a few minutes and then it was just sort of, "meh". Massive anti-climax.
I don't buy into the whole "if dem *****es don't let me play my PC or do what I want, I let dem *****es go!". There is no way I would risk my family to stubbornly keep up an archaic attitude of "no woman tells me what to do". You've got to make your own decision on what's more important. Never being able to play the PC might suck, but not having a family will probably suck harder. We have to live with the situations our past behaviours have placed ourselves in. You at least have an XBOX, it could be worse.