I think you should go for it, whether it's you going there or paying for her to come here.
Like a previous poster said, sisters can't be replaced.
I know it sounds a bit reckless but like you say you are never going to be wealthy anyway any time soon, you have 3 kids, one income, if your DH lost his job you'd kind of be in the shit anyway with you unwell etc, and to be honest, if you were in that situation suddenly, having savings doesn't necessarily do you any favours anyway - I know that sounds awful but the welfare state would see you back on your feet and your savings would get taken into account before that kicked in anyway, and yes, I know that's sort of how it should be but like you say at what point do you put yourself first?
What I am saying is that rightly or wrongly, your children would be fine if your DH lost his job, as the welfare state would see them right, so even if its not the most noble correct thing to do its not like you are gambling your children's future.
I have a similar issue going on in that I want to see my Brother's baby who is due to be born any day now. He lives in Perth, (Oz) and I live here in the UK. It was me who left, I've been here 13 years now but I really want to see that baby. Okay so admittedly with us its not money that stopping us, but I want to go without my children because it would be unfair to decend on them with my 2, plus my 2 are in preschool etc so actually what I want to do is zip over there, spend a week in my home town in Melbourne then go to Perth for 3 days on the "way back" to see the baby. I want to see the baby when its still a baby, and my brother and his partner when they are new parents. But we are reluctant to do the big massive family holiday over there with the 2 kids and my husband etc (which costs about £5k once you've done flights, car seat hire, car hire etc because we'd need a car if we have both kids etc etc) - but its not so much cost its that we don't want to do that massive holiday right now, I'd rather wait a year till my youngest is at least 3 and my son 5 and it would be a lot easier.
Anyway, I digress. My issue is my husband. I wouldn't blink about leaving the kids with my husband, they would love a week with him - (it would be a week plus 2 weekends, essentially) - they are happy as long as they are with one of us. But I feel bad for him having to use a week's worth of annual leave (or perhaps 6/7 days if he picks me up from the airport though I could do it over Easter I guess). But he reckons I should anyway - he said if he really doesn't want to use a weeks worth of leave we could just get a nanny to do the school runs for a week and he could do a mixture of working from home and maybe half days annual leave but actually he doesn't want to do that, he said he may as well go the whole hog and experience a week at home with the kids like I do. But I still feel a bit bad!
But then I think of 24 hours on a plane with several good books and magazines, oh, and duty free shopping
, the deliciousness of sinking into bed with jetlag and being able to sleep till I wake without having to manage the children's jetlag, being able to come and go from my parents house in my home town as I please and- have coffee with ex boyfriends-- no only kidding that's not it honest, but seriously I just think, wow, having been at home for the last 4 years with kids it would be great to have a bit of fun and freedom and catch up with my family as just me, not Tatty + rowdy kids, if you see what I mean?
Its only money, and we are not talking stupid amounts. Do you have any debts? (i.e loans or credit cards)? If you are debt free, I think you should do it. If you are genuinely debt free apart from small car loan or mortgage (I think you said you rented) then I think you should spend your savings on seeing her somehow and worry about the rest later, because if you are debt free and have no mortgage or house to lose, and your DH is in work and whilst no job is ever 100% safe its probably fine and if its not we don't live in a non-welfare state, sod it, just go for it. Rightly or wrongly, that's what I reckon you should do.
So I'm going to do it! Sod it!