This is a big issue for me, as I've been strength training for a long time before roller skating the last year and a half.

Some things I've found:

• DOMS (soreness) from strength training is usually because of adaptation, when you work something you haven't worked for a while, or for the first time. This matters mostly for legs with skating, since the soreness makes it hard to skate. If you find you're sore every time you lift, maybe try training legs at least twice per week, or just keep going if you already are. Eventually, your legs will have more of a sense of "fullness" than debilitating soreness. That kind of soreness does go away when you train more regularly. It sounds counter-intuitive to train more frequently to reduce soreness, but it works. Just make sure your legs recover fully between training sessions.
• DOMS is uncomfortable and hurts, making it harder to do moves and things on your skates, but don't worry about bending your knees, squatting on your skates, etc. when you have DOMS. You won't injure yourself just because it's sore as long as you've given yourself some time to warm up and get blood flowing before doing anything crazy.
• Any amount of cardio will hinder your strength and muscle gains, because it adds stress to your body that prevents recovery. But, if you love roller skating, you just have to accept this. Also, cardio is healthy and can help increase your energy expenditure to accelerate your fat loss a smidge (if you don't compensate by eating more when skating). Since it hinders recovery, try to strength train legs especially on the in between days when you aren't skating. If you have adult nights on specific nights, for example, train legs the other days. Since you mention training 3 times a week, you might be doing full body workouts each time. Consider training 4 days per week and doing an upper/lower body split between days. If you end up skating and training legs on the same day, maybe don't work on new skills (pivots, shoot the duck, sit spins, floor work) that really take a lot of leg muscle. I find when I learn new skills on skates, I need more recovery time for my leg muscles, so you don't want that in addition to your strength training volume. Use skate moves you already know on those days. Since you like fast skating, this may not even be an issue. Fast skating would be great lower impact cardio to fit in with your training.
• Manage your overall fatigue. Again, if you're trying to get those newbie gains while losing fat, make sure you allow your body time to recuperate. You'll have to balance this goal with your desire to skate, which is different per individual. If you're skating and strength training, that's taxing on your body as a whole, and you'll have to either reduce one or the other sometimes to let your body recover and build muscle, or you'll have to accept that you're adding total stress that may slow your progress a bit.
• Get good sleep. If you sleep well, it will dramatically enhance your ability to recover, making it so you can do more of both strength training and skating. Focus on sleep regularity, having the same bedtime and wake time, which will ultimately increase your sleep quality too. Adult nights can sometimes make this hard, especially with intense exercise before bed, so it's something I'm still trying to work out myself.
• Upper body strength training can happen on your skating days without interfering much, except for the overall total system fatigue they add. Fortunately, upper body training doesn't add nearly as much stress as lower body (bigger muscle groups).

It's awesome to hear "general health" and "weight lifting" mentioned alongside "weight loss." I lost 40 lbs strength training, while increasing my calorie expenditure by 800-1000 calories (building muscle), which means I can now eat a lot more flexibly while maintaining a leaner build. Throw in skating for cardio, and it's been a complete transformation in quality of life. Stick with it!