I think offering to take the kids if space is an issue is a good thing to do. I would not think the mother would take you up on your offer, unless you are willing to host her too, until she can get on her feet again. We have learned that, however much they love us and however much more stable our own home may be, the kids want to be with their mother.
It seems more chaotic, looking in, than it feels to the children living in the chaotic situation, I think.
We have taken our grandchildren from time to time. We were good to them, and we all got through it, but the relationship a child has with a young mother (or father) is very different than the relationship established with grandparents.
And, once you are raising the child, your role as a grandparent changes from something very special to the day to day responsibilities of raising the children. husband and I found that going back to the nurturing parent role affected our relationship adversely, too. At a time in our lives when we should have been exploring ourselves, our relationship, new friends and interests, we were back to raising children, again. Breakfast, lunch, dinner, bedtime snacks, special time for friends and carpooling and everything that comes with parenting children were overwhelming to us after having been on our own for a few years. We needed to homeschool too, because we did not have legal guardianship and the local school would not allow us to enroll the kids there. (Crazy, huh? Especially with the taxes we pay, here! Legally, the school system can do that, apparently ~ at least they can, here.)
What we do is keep ourselves mentally prepared to take the kids again if we need to. We all get it though, that the best place for the kids to be is with their mother ~ however crazy it looks to us from the outside. (The kids had abandonment issues when they came to live with us ~ however kind we were, however much more stable our household seemed than the chaos the kids had come out of...kids want to be with their mothers. They do not understand what feels to them like having been sent away.)
We help the family financially, so they can stay together, and so the kids will have what they need. We pay for lessons, we sometimes pay car insurance, we help with school clothes, and we are a back up source of funding in emergencies.
We also functioned as emotional anchors for the kids during the time their worlds were so horribly unstable.
Your role in this child's life can be that of an unwavering source of loving acceptance. Your home can be a place for him or her to go and be welcomed and cherished whatever is happening in the primary residence.
A safe, loving place somewhere in the world where people you trust wait for you and remember you and cherish you.
Our grandchildren are remarkable stable, considering all they have been through. They are wonderful children, growing well and doing well. We are very important to them, and we talk to them almost daily.
But there is no question that the kids want to live with their mother.
Another thing we do to remind the kids that we are out here, loving and thinking about them, even if we haven't seen them lately, is to send little things in the mail frequently.
Sometimes, just a card with a stick or two of chewing gum inside.
So, my take on this is that grandparents can function as irreplaceable sources of safety, love, and encouragement BETTER when the kids do not live with us.
The role of grandparent can sometimes carry more influence than the parenting role we are sometimes required to take on.
Buying clothing, shoes, toys, celebrating the child's birthday with everything special ~ and Christmas, too ~ these are all times a grandparent can function as that warm, safe place a child COULD go, if he needed to.
We can be safe and strong and loving from a distance and still affect the lives of our grandchildren in such positive ways.
That is my advice to you and your husband.
Commit to the child's welfare. Commit yourselves to functioning as the second circle of support for the child, whenever and however it is needed.
We are starting college funds, too.
There are so many things we can do for our grandchildren to make their lives better than they would be if it were only the young parents raising them.