My kids are 7 & 9 (turning 8 & 10 in a couple of months). We've been a dual income household since the kids were infants. Here is my 2 cents on your situation:
1. It sounds like on the days that you are doing your contract nursing gig and DD is sick, your MIL won't babysit...so MIL won't babysit when DD is ill, right? I've gotta say...THAT SUCKS! I lived through that for awhile when my MIL moved to our city when ODD was a year old. MIL was totally keen on babysitting. We had ODD at the time in a full time infant daycare...to the tune of $980/month and that was 9 years ago. We pulled her out of the daycare and MIL babysat full time for awhile. We even paid her for it, so MIL earned a monthly income, too. Every single time ODD came down with a cold or a sniffle, MIL refused to babysit. And then MIL wanted to be able to take weeks off at a time with no advanced notice. So we never got to take any of OUR vacation time off for anything but MIL's out of town trips. Needless to say, within 3 months, it was obvious that it wasn't going to work out. It took another 4 months for me to secure another spot at a daycare.
2. Kids get sick. So if your DD is at an at-home childcare or pretty much anywhere, she's going to get sick. So regardless of what type of job you have, you will likely need to take time off of work to care for her. It sucks a lot when they're really little. By the time they're in 1st grade, though, the monthly illnesses are few and far between. So even if you take the new job that pays $25k more per year, you WILL have to take time off of work to care for a sick child. Just plan on it.
3. You & DH need to negotiate between the 2 of you on this issue, without MIL present. It's a husband & wife decision, not a grandmother decision.
4. I've been in your situation many times before where my DH's job has zero flexibility on time off. Many times, an employer's organization or your immediate supervisor/boss really doesn't give a care about your kid being sick. What makes it really difficult is if BOTH parents have jobs that are inflexible. And if you take the regular 'full time employee' nursing gig, I almost guarantee you that you will be low man on the totem pole. This means that you will likely work most holidays, weekends, etc., you won't get your first pick on shifts, stuff like that.
5. How old is your DD?
6. Daycare is expensive and I'll be honest with you on this....most, if not all, daycare centers do not really have a program set up where you can drop off your child 1 day this week, 2 days next week, etc. You usually have to commit to either full time M-F, 3 days a week, and a few places might have options for 2 days a week. But on the part time daycare options, your child is there on set days and those days don't vary. What I'm trying to tell you is that you won't have the option of doing something like this - next week, you're scheduled to work Mon, Tues, & Wed, so DD goes to daycare on those days. But the following week, you're working Tues, Thurs, & Fri, so you take her to daycare on those days and you only pay for the days that she's there. In reality, you would have to sign her up for full time M-F and pay for it even though you might not actually need it the entire week.
7. If you take the full time job with big salary increase & considering that your work schedule will likely vary a fair amount at first, you & DH will need to adjust things in your DD's social life & extracurricular activites. For example, if the dance class is in the early afternoon, you'll either have to find another dance class, drop the class altogether, or have MIL pick her up from childcare and take her to dance class. Same thing for other planned activities.
8. If there's a possibility that you'll be moving to a different city/state after DH graduates, then it might not be a good idea to take a new full time job, even if it's $24k/year more. It will make it look on your resume like you're flighty or unreliable. Future employers might look at it in a bad light.
In our situation in our family right now, my career growth has been sidelined for a few years and it's been stagnant. But my employer has a great work-life balance sort of attitude about things and I don't get grief for having to leave early to pick up sick children from school. I cannot tell you how valuable that is. DH, on the other hand, has been working hard on growing his career. He just started a new job a month and a half ago and he doesn't even have benefits yet. At his previous work place, if you took ANY days off within the first 6 months of employment, you'd be fired. So I **HAD** to pick up the slack.
I don't think that you necessarily need counseling. You & DH just need to get on the same page on what your mutual goals are and figure out a plan on how to juggle it all.
And by the way, here in my neck of the woods, last-minute babysitters to care for a sick child can cost $15-$20/hour. Regular babysitters cost that much, too. I think it's kind of a lot to ask a friend to watch your child full time. So I disagree a bit with another person's suggestion on that.