I understand your situation. This is my first year that I have no little ones at home to find sitters for so I can volunteer.
Do not take younger siblings on the field trip. The note requests that and there are many reasons for it. I believe this would be the time to call on MIL. Ask her to only help out when there are these big field trips. That means probably 3-5 times in the school year and you would have plenty of advance notice to have her schedule it in. The length of the field trip day would justify and hour drive for her. It would be fabulous grandma time!!!
In the past when my kids were little I always found a couple friends to do weekly babysitting swaps with. In fact, even this year I have two ladies now that we do after kindergarten swap so it lengthens our "free time" on the days we are not on swap duty. Kindergarten here is only 3.5 hours. So two days a a week I have 6 hours and then one day the other 2 ladies' kids come here. It is actually one big playdate for my son. They bring their lunches and have a ball together. The key is finding kids your children get along with..and ladies YOU get along with.(sometimes that is the hard part)
Good luck! Don't feel guilty about not volunteering in the classroom yet. Teachers are understanding...they know what it is like for moms of young kids. Find other ways to volunteer your time. Teachers often need things cut out,traced,papers labled etc. Volunteer to help plan parties or make a class contact list for all parents. I loved when one mom took that job on for my son's 5th grade class last year. The parents gave their email,home address and phone numbers..parents could opt out of giving certain info too. I felt this list was a great way to reach out to parents and kids for playdates, parties, questions about homework or any kind of contact needed.
Good luck and best wishes at finding some time to share your child's school experience together!!