It's a big rise and even if you are able to make it work, it's bound to be a huge financial and emotional adjustment.
Folk have suggested extending the term and interest only as temporary solutions until your childcare costs go down. It's nice to have options in a crisis but if you can manage to weather this storm by reducing other outgoings, I think that would be a wiser step. It's not worth adding years to your mortgage to fund maintaining a lifestyle you can't afford.
I don't know the comparative costs in your area, but sometimes if you have two young children then a nanny or childminder can be more affordable than nursery fees.
Downsizing is a painful (emotionally and financially) option but it is worth taking a good hard look about whether you can afford this house or whether it is going to be a constant source of financial stress and you'd all be happier and more financially secure in a smaller property.
I've found the Ramsey show's baby steps to be helpful. It's US based and a more debt-averse, conservative version of something like Martin Lewis's advice. You can find their radio show/podcast on YouTube.
Their affordability test for housing is a 15 year fixed rate* mortgage where the payments are no more than a quarter of your after tax income.
Leaving aside the term of the mortgage for the moment since you are already in it, I'd look at whether your mortgage payments are going to be a lot over the 25% mark. If it's just going to be tight for a year or two whilst your kids age out of childcare, that's one thing, if the mortgage is going to be a huge burden long term, I don't think it's worth it.
If you have debt other than the mortgage, I'd use your savings to pay it off and free up your monthly income from the repayments. Though obviously in general having an emergency fund is a good thing.
High outgoings can mean that even folk on high salaries can have money stress, the good news is that you've got options.
- Ramey really recommend a long term fixed rate to stabilise your biggest expense, variable rates are for the mortgage company's benefit. You can always refinance if rates come down substantially. 15 years, because their principles are about freeing up your income from payments rather than living in perpetual debt - many of their followers pay off the mortgage early.