Advice on calories and exercises to gain muscle

I'm 34, 5ft 4, 108lb (7st 10) which is a bmi 18.4 with apparently a body fat % of 21. I eat healthily and can't eat massive portions.

I swim/cross train 2 or 3 times a week&walk 5-7miles a day on school runs etc. I am pretty fit and everyone comments on how fast I walk etc. However, I'm not strong and I really want to build up muscle so I can lift my children etc without hurting my back/neck. I am prone to those injuries and often see an osteopath.

The only strength exercises I do at the moment are 1hour of pilates a week after being recommended it by a physio. I know I need to eat more protein and eat a calorie surplus and start doing some weights but what would that be for my stats? Do I need to choose a gaining weight target? Or just eat a bit more than maintenance? And how often should I cross train/swim vs weights? I only have dumbells and need it to be done at home as I have small children&don't have the time/money to go to a gym or classes.

Sorry if these seem like dumb questions but I've never done weights and I hope I've given enough info for someone to help. Thanks