My father in law died a month ago and I’ve just spent the week in the US for work, in hindsight it was a mistake to go away and leave my girlfriend.
She had family around and stuff but still wasn’t good, especially with 8 hours time difference. By your original post it sounds like you’re more concerned about looking after your mum. Indeed she might take longer to get over it as she’ll have to readjust to day to day life without him bit don’t neglect yourself and your grief. Even the closest families can have silly arguments in times of stress, be ready for them and let anything go that doesn’t compromise your principles. We learnt that the hard way.
Best of luck, it’s a grim time for everyone but you should have a few laughs along the way finding out things about your dad you never knew!